Summarized EDA
Read in the data set data types
covid <- read.csv(text=getURL("https://raw.githubusercontent.com/C-Stewart-GH/Time_Series_Project/main/Raw_Data_Files/merged_data.csv"))
covid$Date=mdy(covid$Date)
str(covid)
## 'data.frame': 416 obs. of 10 variables:
## $ Date : Date, format: "2020-09-14" "2020-09-15" ...
## $ tests_taken : int 34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
## $ case_count : int 3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
## $ retail_and_recreation_percent_change_from_baseline: int -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
## $ grocery_and_pharmacy_percent_change_from_baseline : int -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
## $ parks_percent_change_from_baseline : int 1 7 7 16 6 21 -6 -29 -28 -9 ...
## $ transit_stations_percent_change_from_baseline : int -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
## $ workplaces_percent_change_from_baseline : int -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
## $ residential_percent_change_from_baseline : int 9 10 10 10 9 3 4 12 15 12 ...
## $ vaccine_doses_administered : int 0 0 0 0 0 0 0 0 0 0 ...
summary(covid)
## Date tests_taken case_count
## Min. :2020-09-14 Min. : 0 Min. : 45
## 1st Qu.:2020-12-26 1st Qu.: 61048 1st Qu.: 2325
## Median :2021-04-09 Median : 92026 Median : 4661
## Mean :2021-04-09 Mean : 95723 Mean : 6876
## 3rd Qu.:2021-07-22 3rd Qu.:126984 3rd Qu.:10311
## Max. :2021-11-03 Max. :268222 Max. :28027
## retail_and_recreation_percent_change_from_baseline
## Min. :-78.00
## 1st Qu.:-16.00
## Median : -9.00
## Mean :-11.65
## 3rd Qu.: -6.00
## Max. : 6.00
## grocery_and_pharmacy_percent_change_from_baseline
## Min. :-55.000
## 1st Qu.: -9.000
## Median : -4.000
## Mean : -4.442
## 3rd Qu.: 1.000
## Max. : 29.000
## parks_percent_change_from_baseline
## Min. :-76.000
## 1st Qu.:-16.000
## Median : -3.000
## Mean : -5.724
## 3rd Qu.: 6.000
## Max. : 30.000
## transit_stations_percent_change_from_baseline
## Min. :-68.00
## 1st Qu.:-26.00
## Median :-16.00
## Mean :-18.01
## 3rd Qu.:-10.00
## Max. : 0.00
## workplaces_percent_change_from_baseline
## Min. :-86.00
## 1st Qu.:-33.00
## Median :-29.00
## Mean :-27.25
## 3rd Qu.:-16.75
## Max. : -7.00
## residential_percent_change_from_baseline vaccine_doses_administered
## Min. :-1.000 Min. : 0
## 1st Qu.: 5.000 1st Qu.: 18829
## Median : 7.000 Median : 63698
## Mean : 7.288 Mean : 81305
## 3rd Qu.: 9.000 3rd Qu.:104878
## Max. :29.000 Max. :374014
cases=read.csv(text=getURL("https://raw.githubusercontent.com/C-Stewart-GH/Time_Series_Project/main/Raw_Data_Files/Texas%20COVID-19%20Case%20Count%20Data%20by%20County.csv"))
cases$Date=mdy(cases$Date)
cases$Case.Count=c(NA,diff(cases$Case.Count))
cases=cases[2:length(cases$Date),]
str(cases)
## 'data.frame': 611 obs. of 2 variables:
## $ Date : Date, format: "2020-03-05" "2020-03-06" ...
## $ Case.Count: int 0 5 0 0 7 3 3 4 0 0 ...
Plot reduced and full data and check for consistent covariance
plotts.sample.wge(covid$case_count,lag.max = 100,trunc = 35)

## $autplt
## [1] 1.000000000 0.742528247 0.568188353 0.568594327 0.576982271
## [6] 0.569425145 0.701936212 0.788346677 0.670085415 0.549747319
## [11] 0.550653544 0.541369785 0.520023441 0.613463198 0.686238834
## [16] 0.579105471 0.475534601 0.479380813 0.450467986 0.434639425
## [21] 0.511259716 0.571558900 0.484968510 0.387938490 0.369553508
## [26] 0.356754837 0.330746556 0.423751392 0.490012795 0.377929103
## [31] 0.250386855 0.234576763 0.244437559 0.230451758 0.302175735
## [36] 0.341339575 0.244001358 0.141616768 0.129190829 0.137548097
## [41] 0.133370112 0.190744990 0.222369375 0.138301667 0.068050640
## [46] 0.068718459 0.042690803 0.034864433 0.088966626 0.124168606
## [51] 0.047142091 -0.013793944 -0.005246058 -0.006333880 -0.037576153
## [56] 0.013757960 0.048489410 -0.011703692 -0.076379088 -0.069127874
## [61] -0.075131620 -0.088294390 -0.050668572 -0.029211398 -0.084167395
## [66] -0.132178208 -0.135934445 -0.144845032 -0.142898050 -0.113375908
## [71] -0.080610695 -0.123443259 -0.164019315 -0.158974635 -0.168804967
## [76] -0.194097063 -0.161856993 -0.136231418 -0.175128917 -0.202941176
## [81] -0.192376059 -0.192316547 -0.204487542 -0.183439209 -0.158478309
## [86] -0.186326837 -0.233922192 -0.223170036 -0.218729881 -0.234557086
## [91] -0.212228469 -0.183881154 -0.204548312 -0.233565249 -0.245103441
## [96] -0.251428011 -0.258432767 -0.223506684 -0.181614570 -0.208993778
## [101] -0.242637258
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 15.3915975 18.4632526 11.2853210 11.0716564 0.3093163 4.9499390
## [7] 2.0109647 0.4500694 -8.8568076 -7.7816920 -16.2112771 -5.1474908
## [13] -4.3890008 -9.3369436 -0.7862864 -3.7681382 -6.2752053 -12.3708249
## [19] -4.4332477 -28.0916503 -5.8310822 -15.3195884 -14.1401708 -14.6743049
## [25] -14.9448720 -21.3642778 -38.2589161 -5.9216012 -1.8099687 -10.4638673
## [31] -4.4354118 -35.4157764 -14.8011192 -6.2561408 -3.8950515 -10.8533207
## [37] -7.6537160 -14.4593527 -11.3330937 -5.9793930 -3.5008067 -8.1084935
## [43] -17.7647573 -7.8158450 -11.6786247 -1.7831609 -0.6907818 -5.6565398
## [49] -2.8314629 -13.8965331 0.2349314 -3.5370873 -10.2305864 -4.0536018
## [55] -5.9246423 0.9755728 -4.4226530 4.5916244 9.9584147 -2.4912398
## [61] 7.2710740 2.5987828 -2.9453740 -1.8352426 -5.5600948 -13.3310388
## [67] -6.8021784 -8.5531231 -5.3218649 -7.2003684 -2.3388024 0.6952226
## [73] -5.8407752 -1.8277963 -1.9053610 -7.1484594 -4.7470266 -8.7136451
## [79] -4.4813375 -18.7421273 -6.7853728 -49.5661075 -12.8856800 -11.1383088
## [85] -2.0006269 -11.1693950 -5.3939753 -5.1994213 -14.8737813 -4.0758832
## [91] -5.5409990 -5.4659455 -5.7376952 -9.5106980 -7.0640107 -10.4334016
## [97] -7.7547565 -12.8322066 -13.9305763 -12.2960066 -10.0585227 -5.6928946
## [103] -2.7778360 -2.2893742 -11.6249579 -6.9351941 -7.1960405 -14.1564481
## [109] -18.4128344 -6.3217552 -6.1256032 -6.2857096 -7.2415358 -5.3985614
## [115] -3.9401621 -2.8056642 1.3802605 -5.3714900 7.5278018 1.8423490
## [121] -0.3541421 -1.5330337 -8.5118989 -4.6759078 -5.5057884 -7.0399737
## [127] -4.4531419 -13.8441388 -2.1971540 -28.0081310 -3.3873168 -10.8405235
## [133] -7.0521061 -25.3589631 -4.5258446 -11.1463496 -8.6616418 -11.9312307
## [139] -13.7477494 -13.7026912 -5.8494544 -7.1039012 -21.2409298 -9.1678052
## [145] -16.2015037 -6.7772933 -11.4192224 -2.6917797 -10.2853156 -10.3603815
## [151] -6.6987701 -13.2684788 -7.0554776 -11.4996202 -12.1916695 -8.7912438
## [157] -15.4502721 -6.2453446 -14.3429745 -10.4618932 -13.3261658 -16.9944583
## [163] -15.3686823 -16.7002621 -22.0137817 -4.8536474 -13.0412320 -8.9138482
## [169] -8.2819848 -9.3758574 -7.8875518 -10.0059583 -10.8398176 -11.6710773
## [175] -12.6553806 -10.2877806 -8.8393494 -9.2518667 -7.8700539 -8.3434222
## [181] -6.6963098 -8.7142459 -7.7126224 -15.9373668 -9.7782580 -6.9771035
## [187] -21.0147620 -9.5746777 -23.7636124 -8.6439000 -8.1495797 -19.8339974
## [193] -12.1937912 -8.6442698 -5.5039774 -7.4264241 -7.2929577 -7.1695303
## [199] -13.3734137 -9.8948865 -9.9663371 -6.7578743 -9.3868384 -9.3159440
## [205] -5.7463010 -19.1656268 -9.8296369 -26.5219166
##
## $dbz
## [1] 12.02854192 11.89716070 11.67763423 11.36912898 10.97048679
## [6] 10.48023988 9.89664107 9.21772099 8.44139215 7.56563340
## [11] 6.58881029 5.51022385 4.33103726 3.05581103 1.69496392
## [16] 0.26847703 -1.18920694 -2.62445923 -3.96409094 -5.12617168
## [21] -6.04485743 -6.69677511 -7.10646502 -7.32599226 -7.40870444
## [26] -7.39535728 -7.31360706 -7.18324206 -7.02096705 -6.84247427
## [31] -6.66217771 -6.49190641 -6.33964443 -6.20882244 -6.09820664
## [36] -6.00223487 -5.91164133 -5.81427995 -5.69613012 -5.54251745
## [41] -5.33958229 -5.07595761 -4.74446755 -4.34348765 -3.87754481
## [46] -3.35689330 -2.79614563 -2.21236675 -1.62315879 -1.04514249
## [51] -0.49300501 0.02092098 0.48668804 0.89653339 1.24457518
## [56] 1.52649133 1.73922961 1.88077252 1.94996596 1.94641343
## [61] 1.87043569 1.72309532 1.50628683 1.22289214 0.87699837
## [66] 0.47416528 0.02171216 -0.47103606 -0.99264357 -1.52973935
## [71] -2.06762524 -2.59140742 -3.08757613 -3.54571176 -3.95979491
## [76] -4.32861734 -4.65509647 -4.94473669 -5.20378903 -5.43768133
## [81] -5.65008637 -5.84272723 -6.01580802 -6.16883191 -6.30151579
## [86] -6.41452308 -6.50981615 -6.59056184 -6.66066581 -6.72410772
## [91] -6.78427148 -6.84341945 -6.90238168 -6.96045378 -7.01544033
## [96] -7.06375125 -7.10046163 -7.11928515 -7.11249036 -7.07089586
## [101] -6.98418053 -6.84176747 -6.63440393 -6.35623421 -6.00676740
## [106] -5.59195858 -5.12388280 -4.61909183 -4.09629120 -3.57411231
## [111] -3.06949787 -2.59684037 -2.16774526 -1.79119320 -1.47389558
## [116] -1.22070105 -1.03497228 -0.91889625 -0.87371622 -0.89988588
## [121] -0.99714994 -1.16455530 -1.40039523 -1.70208711 -2.06598419
## [126] -2.48712547 -2.95893755 -3.47292132 -4.01838832 -4.58235290
## [131] -5.14972726 -5.70397562 -6.22831845 -6.70740497 -7.12912566
## [136] -7.48604751 -7.77599377 -8.00160298 -8.16911960 -8.28692414
## [141] -8.36427539 -8.41050094 -8.43461916 -8.44523030 -8.45049351
## [146] -8.45806375 -8.47493914 -8.50722845 -8.55987547 -8.63637947
## [151] -8.73854045 -8.86624852 -9.01733543 -9.18751602 -9.37046415
## [156] -9.55808350 -9.74103377 -9.90953972 -10.05443423 -10.16827976
## [161] -10.24632252 -10.28702316 -10.29201227 -10.26550181 -10.21335268
## [166] -10.14207025 -10.05795912 -9.96656238 -9.87240222 -9.77896619
## [171] -9.68885285 -9.60399054 -9.52585917 -9.45566648 -9.39445187
## [176] -9.34311029 -9.30234372 -9.27255885 -9.25373608 -9.24529770
## [181] -9.24600371 -9.25390262 -9.26636170 -9.28019560 -9.29190153
## [186] -9.29799210 -9.29539366 -9.28185390 -9.25628645 -9.21898106
## [191] -9.17163047 -9.11716413 -9.05942028 -9.00271769 -8.95139712
## [196] -8.90939240 -8.87987004 -8.86495523 -8.86554764 -8.88122495
## [201] -8.91023472 -8.94958186 -8.99522469 -9.04239227 -9.08602372
## [206] -9.12130513 -9.14424544 -9.15220086
plotts.sample.wge(cases$Case.Count,lag.max = 40,trunc = 35)

## $autplt
## [1] 1.0000000 0.7812711 0.6346308 0.6347067 0.6402183 0.6331306 0.7429388
## [8] 0.8146490 0.7112276 0.6062146 0.6092684 0.5990211 0.5802352 0.6559966
## [15] 0.7155404 0.6232571 0.5353154 0.5365204 0.5139853 0.4970087 0.5586768
## [22] 0.6081906 0.5300153 0.4461105 0.4321604 0.4212868 0.3978909 0.4724666
## [29] 0.5278958 0.4278843 0.3208573 0.3087146 0.3144161 0.2986608 0.3593858
## [36] 0.3906941 0.3057663 0.2167749 0.2066178 0.2117197 0.2038381
##
## $freq
## [1] 0.001636661 0.003273322 0.004909984 0.006546645 0.008183306 0.009819967
## [7] 0.011456628 0.013093290 0.014729951 0.016366612 0.018003273 0.019639935
## [13] 0.021276596 0.022913257 0.024549918 0.026186579 0.027823241 0.029459902
## [19] 0.031096563 0.032733224 0.034369885 0.036006547 0.037643208 0.039279869
## [25] 0.040916530 0.042553191 0.044189853 0.045826514 0.047463175 0.049099836
## [31] 0.050736498 0.052373159 0.054009820 0.055646481 0.057283142 0.058919804
## [37] 0.060556465 0.062193126 0.063829787 0.065466448 0.067103110 0.068739771
## [43] 0.070376432 0.072013093 0.073649755 0.075286416 0.076923077 0.078559738
## [49] 0.080196399 0.081833061 0.083469722 0.085106383 0.086743044 0.088379705
## [55] 0.090016367 0.091653028 0.093289689 0.094926350 0.096563011 0.098199673
## [61] 0.099836334 0.101472995 0.103109656 0.104746318 0.106382979 0.108019640
## [67] 0.109656301 0.111292962 0.112929624 0.114566285 0.116202946 0.117839607
## [73] 0.119476268 0.121112930 0.122749591 0.124386252 0.126022913 0.127659574
## [79] 0.129296236 0.130932897 0.132569558 0.134206219 0.135842881 0.137479542
## [85] 0.139116203 0.140752864 0.142389525 0.144026187 0.145662848 0.147299509
## [91] 0.148936170 0.150572831 0.152209493 0.153846154 0.155482815 0.157119476
## [97] 0.158756137 0.160392799 0.162029460 0.163666121 0.165302782 0.166939444
## [103] 0.168576105 0.170212766 0.171849427 0.173486088 0.175122750 0.176759411
## [109] 0.178396072 0.180032733 0.181669394 0.183306056 0.184942717 0.186579378
## [115] 0.188216039 0.189852700 0.191489362 0.193126023 0.194762684 0.196399345
## [121] 0.198036007 0.199672668 0.201309329 0.202945990 0.204582651 0.206219313
## [127] 0.207855974 0.209492635 0.211129296 0.212765957 0.214402619 0.216039280
## [133] 0.217675941 0.219312602 0.220949264 0.222585925 0.224222586 0.225859247
## [139] 0.227495908 0.229132570 0.230769231 0.232405892 0.234042553 0.235679214
## [145] 0.237315876 0.238952537 0.240589198 0.242225859 0.243862520 0.245499182
## [151] 0.247135843 0.248772504 0.250409165 0.252045827 0.253682488 0.255319149
## [157] 0.256955810 0.258592471 0.260229133 0.261865794 0.263502455 0.265139116
## [163] 0.266775777 0.268412439 0.270049100 0.271685761 0.273322422 0.274959083
## [169] 0.276595745 0.278232406 0.279869067 0.281505728 0.283142390 0.284779051
## [175] 0.286415712 0.288052373 0.289689034 0.291325696 0.292962357 0.294599018
## [181] 0.296235679 0.297872340 0.299509002 0.301145663 0.302782324 0.304418985
## [187] 0.306055646 0.307692308 0.309328969 0.310965630 0.312602291 0.314238953
## [193] 0.315875614 0.317512275 0.319148936 0.320785597 0.322422259 0.324058920
## [199] 0.325695581 0.327332242 0.328968903 0.330605565 0.332242226 0.333878887
## [205] 0.335515548 0.337152209 0.338788871 0.340425532 0.342062193 0.343698854
## [211] 0.345335516 0.346972177 0.348608838 0.350245499 0.351882160 0.353518822
## [217] 0.355155483 0.356792144 0.358428805 0.360065466 0.361702128 0.363338789
## [223] 0.364975450 0.366612111 0.368248773 0.369885434 0.371522095 0.373158756
## [229] 0.374795417 0.376432079 0.378068740 0.379705401 0.381342062 0.382978723
## [235] 0.384615385 0.386252046 0.387888707 0.389525368 0.391162029 0.392798691
## [241] 0.394435352 0.396072013 0.397708674 0.399345336 0.400981997 0.402618658
## [247] 0.404255319 0.405891980 0.407528642 0.409165303 0.410801964 0.412438625
## [253] 0.414075286 0.415711948 0.417348609 0.418985270 0.420621931 0.422258592
## [259] 0.423895254 0.425531915 0.427168576 0.428805237 0.430441899 0.432078560
## [265] 0.433715221 0.435351882 0.436988543 0.438625205 0.440261866 0.441898527
## [271] 0.443535188 0.445171849 0.446808511 0.448445172 0.450081833 0.451718494
## [277] 0.453355155 0.454991817 0.456628478 0.458265139 0.459901800 0.461538462
## [283] 0.463175123 0.464811784 0.466448445 0.468085106 0.469721768 0.471358429
## [289] 0.472995090 0.474631751 0.476268412 0.477905074 0.479541735 0.481178396
## [295] 0.482815057 0.484451718 0.486088380 0.487725041 0.489361702 0.490998363
## [301] 0.492635025 0.494271686 0.495908347 0.497545008 0.499181669
##
## $db
## [1] 14.62709679 17.66972280 19.44130136 8.63611551 11.81032626
## [6] 10.58683206 0.53096424 0.33956666 5.56220004 0.50807722
## [11] -0.03016602 -2.54607832 -3.38349759 -9.33475042 -3.72139665
## [16] -9.97248906 -3.94143961 -7.70399371 -7.74273558 -8.41407286
## [21] -7.06834990 -2.39039445 -3.35968633 -4.61169504 -5.20210169
## [26] -14.85683910 -5.23170793 -6.82390607 -18.79048940 -11.29676156
## [31] -9.26662912 -14.07080281 -7.16048983 -19.30295606 -11.97498329
## [36] -23.54570111 -11.70061950 -19.60362530 -9.19077953 -8.73955794
## [41] -8.26136807 -10.42500125 -2.19652312 -7.95617140 -9.21569461
## [46] -6.71890817 -14.80945347 -7.97055245 -7.68579286 -6.62652719
## [51] -6.04794563 -6.87772196 -10.88186079 -8.90593137 -9.46881046
## [56] -14.23880279 -12.64471994 -8.02844287 -6.20433312 -4.51686572
## [61] -6.18996066 -9.23724972 -12.17901052 -10.64706953 -8.62285332
## [66] -27.10851865 -2.65380459 -3.39470522 -1.15630178 -2.22651048
## [71] -12.63608233 -4.33530561 -6.30622899 -1.96304916 -1.66647298
## [76] -11.98019759 -3.82421762 -10.78402139 -8.72636725 -2.81118364
## [81] -4.33490577 -0.83940855 -3.85023746 0.83212169 3.80590102
## [86] -1.53945251 10.41911230 0.03206521 6.98423165 3.11487819
## [91] -0.60313104 3.90391550 -9.63255559 -4.73313503 -12.77455294
## [96] -7.59093410 -13.13029719 -10.12099447 -7.12184145 -6.34585155
## [101] -2.46358288 -21.12618285 -8.05932984 -1.71664425 -3.51790657
## [106] -0.22585865 -5.98483206 -3.03063696 -3.88811320 -4.52314764
## [111] -0.85509069 -6.68427027 -6.19412958 -7.40122679 -35.79467978
## [116] -6.15369558 -12.28574288 -11.43307162 -7.31077480 -9.72921632
## [121] -8.28306634 -12.27872149 -8.25189953 -9.52522379 -4.27686486
## [126] -13.29499404 -4.39471067 -8.94510381 -11.13272404 -2.89593921
## [131] -14.50906082 -5.19294714 -9.33734735 -6.36883594 -8.86449931
## [136] -6.35835688 -6.92365564 -12.52404167 -4.05762792 -12.10583366
## [141] -11.84879029 -11.52412239 -13.06121719 -13.47502444 -17.29500101
## [146] -12.15963994 -12.98213491 -10.48199513 -11.26558060 -5.60690600
## [151] -3.04585224 -4.50634657 -3.58506672 -10.97137959 -9.11281979
## [156] -9.40296469 -8.43519247 -11.37893228 -9.00884007 -17.17442328
## [161] -5.79269086 -15.18330991 -6.88904152 -8.85095359 -6.82297906
## [166] -6.83843573 -4.23033245 -6.28156129 -6.96235543 -3.28865690
## [171] -4.99588869 0.29200008 -2.23354195 5.81459498 5.62517223
## [176] 0.38330692 1.22509076 -2.99292728 -1.79293783 -3.53914537
## [181] -13.52961069 -4.42160445 -11.68298223 -6.03073232 -6.33964697
## [186] -7.79206172 -4.38984254 -13.31866780 -3.96602837 -5.40521993
## [191] -20.47013392 -5.29967173 -6.09161742 -6.63061983 -8.16489147
## [196] -8.92924276 -12.81654691 -5.57754032 -12.49596456 -8.71549833
## [201] -10.28106562 -11.71620335 -8.94452709 -15.31181754 -20.00398085
## [206] -10.28958894 -7.29216861 -6.78350613 -10.00153111 -24.32675377
## [211] -16.19765744 -7.34459659 -22.32812809 -9.39338512 -7.02077476
## [216] -11.25310975 -5.72307048 -5.28025403 -9.35587729 -12.56860630
## [221] -11.01304568 -5.61036530 -13.62952214 -8.34460152 -9.42209017
## [226] -14.47320416 -13.85342319 -14.22322404 -11.86388047 -13.26939845
## [231] -9.33298905 -6.18024160 -17.27425279 -10.31914137 -11.02260568
## [236] -17.67425789 -7.13784421 -35.52434548 -18.89126609 -19.75915030
## [241] -15.45223599 -22.31646645 -8.80754567 -5.31653385 -15.59976761
## [246] -10.60483844 -9.82938708 -11.39793692 -5.53129018 -16.66832288
## [251] -9.96233948 -7.92086880 -16.06172675 -12.58369718 -9.63964764
## [256] -17.95293811 -12.93808221 -7.53701667 -25.67800933 -13.07030558
## [261] -14.49934213 -3.99575794 -12.65966913 -8.03159487 -7.80131065
## [266] -8.24366045 -12.62415663 -7.26212919 -8.93149752 -22.74945560
## [271] -8.24041644 -16.03212532 -8.89991657 -10.78696538 -13.62288273
## [276] -10.93385321 -12.98590185 -13.73108300 -9.99356142 -14.07588377
## [281] -8.35388422 -19.38723303 -14.46799529 -11.09829209 -9.78613322
## [286] -9.13652598 -4.54671893 -10.17326821 -11.26769421 -5.14992861
## [291] -9.94260634 -16.49955848 -15.02661418 -9.34631459 -12.85398952
## [296] -7.25463929 -9.36978257 -9.54720165 -8.92047917 -12.30571824
## [301] -8.27353007 -9.09171526 -9.60823546 -16.15189774 -8.75532180
##
## $dbz
## [1] 12.39311114 12.33138513 12.22838209 12.08391267 11.89771228
## [6] 11.66944185 11.39868921 11.08497150 10.72773908 10.32638181
## [11] 9.88023877 9.38861295 8.85079326 8.26608702 7.63386743
## [16] 6.95364254 6.22515454 5.44852196 4.62444102 3.75446751
## [21] 2.84140360 1.88981317 0.90667584 -0.09784864 -1.10965720
## [26] -2.11019580 -3.07664515 -3.98335199 -4.80487151 -5.52028369
## [31] -6.11740750 -6.59498805 -6.96169762 -7.23252581 -7.42440509
## [36] -7.55281879 -7.63013726 -7.66548865 -7.66554685 -7.63561795
## [41] -7.58058932 -7.50551828 -7.41581663 -7.31710948 -7.21490346
## [46] -7.11419965 -7.01914996 -6.93280854 -6.85699072 -6.79222796
## [51] -6.73779849 -6.69181420 -6.65134948 -6.61260386 -6.57109444
## [56] -6.52187605 -6.45978627 -6.37970978 -6.27685258 -6.14701279
## [61] -5.98683098 -5.79400162 -5.56742677 -5.30729660 -5.01508675
## [66] -4.69347129 -4.34616024 -3.97767993 -3.59312111 -3.19788165
## [71] -2.79742786 -2.39709199 -2.00191568 -1.61654156 -1.24514922
## [76] -0.89142852 -0.55858159 -0.24934484 0.03397644 0.28946705
## [81] 0.51555890 0.71098952 0.87476388 1.00612114 1.10450696
## [86] 1.16955170 1.20105476 1.19897516 1.16342830 1.09468898
## [91] 0.99320083 0.85959207 0.69469769 0.49958773 0.27560114
## [96] 0.02438406 -0.25206974 -0.55137942 -0.87074392 -1.20692192
## [101] -1.55623393 -1.91459669 -2.27760017 -2.64063482 -2.99907083
## [106] -3.34848181 -3.68489322 -4.00502460 -4.30648767 -4.58790411
## [111] -4.84891862 -5.09010220 -5.31276191 -5.51869057 -5.70989722
## [116] -5.88835743 -6.05581301 -6.21363844 -6.36277917 -6.50375733
## [121] -6.63673361 -6.76160993 -6.87815484 -6.98613325 -7.08542266
## [126] -7.17610122 -7.25849747 -7.33319762 -7.40101273 -7.46291348
## [131] -7.51994405 -7.57312797 -7.62337774 -7.67141771 -7.71772577
## [136] -7.76249603 -7.80562108 -7.84668974 -7.88499446 -7.91954171
## [141] -7.94905916 -7.97199503 -7.98650836 -7.99045314 -7.98136491
## [146] -7.95646363 -7.91269107 -7.84680199 -7.75552446 -7.63579356
## [151] -7.48504572 -7.30153973 -7.08465310 -6.83509563 -6.55499206
## [156] -6.24781178 -5.91815713 -5.57145156 -5.21358434 -4.85056705
## [161] -4.48824318 -4.13207209 -3.78699118 -3.45734722 -3.14688174
## [166] -2.85875410 -2.59558758 -2.35952678 -2.15229822 -1.97526862
## [171] -1.82949760 -1.71578315 -1.63469932 -1.58662579 -1.57176977
## [176] -1.59018051 -1.64175664 -1.72624672 -1.84324306 -1.99216892
## [181] -2.17225912 -2.38253408 -2.62176759 -2.88844887 -3.18074003
## [186] -3.49643120 -3.83289665 -4.18705697 -4.55535473 -4.93375244
## [191] -5.31776373 -5.70252834 -6.08293912 -6.45382379 -6.81017413
## [196] -7.14740389 -7.46160468 -7.74976245 -8.00989881 -8.24111302
## [201] -8.44352025 -8.61810255 -8.76650511 -8.89081698 -8.99337142
## [206] -9.07658974 -9.14287888 -9.19458009 -9.23395750 -9.26321091
## [211] -9.28449751 -9.29994929 -9.31167791 -9.32176289 -9.33222348
## [216] -9.34497700 -9.36178867 -9.38421769 -9.41356450 -9.45082278
## [221] -9.49663901 -9.55128162 -9.61462106 -9.68612233 -9.76485130
## [226] -9.84949643 -9.93840778 -10.02965449 -10.12110110 -10.21050171
## [231] -10.29560798 -10.37428489 -10.44462515 -10.50505163 -10.55439704
## [236] -10.59195195 -10.61747608 -10.63117259 -10.63363039 -10.62574341
## [241] -10.60861811 -10.58348059 -10.55159303 -10.51418643 -10.47241318
## [246] -10.42732030 -10.37984125 -10.33080304 -10.28094400 -10.23093763
## [251] -10.18141786 -10.13300200 -10.08630824 -10.04196567 -10.00061584
## [256] -9.96290578 -9.92947311 -9.90092475 -9.87781067 -9.86059485
## [261] -9.84962514 -9.84510397 -9.84706158 -9.85533349 -9.86954361
## [266] -9.88909481 -9.91316832 -9.94073367 -9.97057058 -10.00130380
## [271] -10.03145133 -10.05948528 -10.08390315 -10.10330590 -10.11647728
## [276] -10.12245789 -10.12060685 -10.11064473 -10.09267272 -10.06716607
## [281] -10.03494219 -9.99710731 -9.95498711 -9.91004830 -9.86381781
## [286] -9.81780566 -9.77343587 -9.73198832 -9.69455279 -9.66199543
## [291] -9.63493696 -9.61374162 -9.59851588 -9.58911590 -9.58516318
## [296] -9.58606799 -9.59106016 -9.59922717 -9.60955874 -9.62099711
## [301] -9.63249135 -9.64305338 -9.65181268 -9.65806630 -9.66132047
acf(cases$Case.Count[1:(length(cases$Case.Count)/2)],lag.max = 40)
acf(cases$Case.Count[(length(cases$Case.Count)/2+1):length(cases$Case.Count)],lag.max = 40)
acf(covid$case_count[1:(length(covid$case_count)/2)],lag.max = 60)
acf(covid$case_count[(length(covid$case_count)/2+1):length(covid$case_count)],lag.max = 60)

Assume you remove seasonality first
fcases_s7=artrans.wge(cases$Case.Count,phi.tr = c(rep(0,6),1),lag.max = 30)

pcases_s7=artrans.wge(covid$case_count,phi.tr = c(rep(0,6),1),lag.max = 60)

#Dicky-Fuller Test shows d=1 does not belong in the data after adding s=7
adf.test(fcases_s7)
## Warning in adf.test(fcases_s7): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: fcases_s7
## Dickey-Fuller = -6.7219, Lag order = 8, p-value = 0.01
## alternative hypothesis: stationary
#We can see the remaining data is not white noise from the ACF
full_s7=plotts.sample.wge(fcases_s7,lag.max = 50,arlimits = T)

#Use overfit to detect any additional seasonality, none found
factor.wge(phi = c(rep(0,6),1))
##
## Coefficients of Original polynomial:
## 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
##
## Factor Roots Abs Recip System Freq
## 1-1.0000B 1.0000 1.0000 0.0000
## 1+0.4450B+1.0000B^2 -0.2225+-0.9749i 1.0000 0.2857
## 1-1.2470B+1.0000B^2 0.6235+-0.7818i 1.0000 0.1429
## 1+1.8019B+1.0000B^2 -0.9010+-0.4339i 1.0000 0.4286
##
##
est.ar.wge(fcases_s7,p = 17,type = "burg")[0]
##
## Coefficients of Original polynomial:
## 0.3600 -0.0661 0.0457 0.0738 0.0193 0.2059 -0.5236 0.2910 -0.0138 0.0847 0.0778 -0.0011 0.1181 -0.2465 0.1050 -0.0037 0.0812
##
## Factor Roots Abs Recip System Freq
## 1+1.8623B+0.8828B^2 -1.0547+-0.1425i 0.9396 0.4786
## 1-0.9279B 1.0777 0.9279 0.0000
## 1-0.7318B+0.8579B^2 0.4265+-0.9919i 0.9262 0.1854
## 1-0.2039B+0.8414B^2 0.1211+-1.0834i 0.9173 0.2323
## 1+1.2719B+0.8028B^2 -0.7922+-0.7862i 0.8960 0.3756
## 1-1.4386B+0.8012B^2 0.8977+-0.6649i 0.8951 0.1015
## 1+0.8914B+0.7636B^2 -0.5837+-0.9843i 0.8739 0.3352
## 1-1.5750B+0.7165B^2 1.0991+-0.4331i 0.8465 0.0597
## 1+0.4916B+0.3902B^2 -0.6298+-1.4717i 0.6247 0.3144
##
##
## named list()
#Show there is white noise remaining (p=0 so null is rejected)
ljung.wge(fcases_s7,K = 24)$pval
## Obs 0.266423 0.05373704 0.03211946 0.1132684 0.1335679 0.1335933 -0.241367 0.05224615 0.1214119 0.1352167 0.1252028 0.08708691 0.03062759 0.02477118 0.01718876 0.05536113 0.09434068 0.02828528 0.05230759 -0.02482603 -0.07102701 0.03072618 0.1080432 0.06055197
## [1] 0
ljung.wge(fcases_s7,K = 48)$pval
## Obs 0.266423 0.05373704 0.03211946 0.1132684 0.1335679 0.1335933 -0.241367 0.05224615 0.1214119 0.1352167 0.1252028 0.08708691 0.03062759 0.02477118 0.01718876 0.05536113 0.09434068 0.02828528 0.05230759 -0.02482603 -0.07102701 0.03072618 0.1080432 0.06055197 0.04611405 0.005339406 0.08050327 0.166298 0.06317725 -0.05226114 -0.05449128 -0.005420944 -0.004724705 -0.002154415 -0.05919043 -0.0311847 -0.06392585 -0.09126132 -0.0197438 0.007086993 -0.02664173 -0.0395837 -0.04490998 0.02728073 0.04205537 -0.08572992 -0.03978426 -0.04199721
## [1] 0
#Use aic5 to find remaining correlation
acf(fcases_s7,lag.max = 60)
pacf(fcases_s7,lag.max = 60)
# aic5.wge(x = fcases_s7,p = 11:20,q = 4:9,type = 'bic')
# aic5.wge(x = fcases_s7,p = 2,q = 9:14,type = 'aic')
#Models based on full data
est_fcases_s7p21q8=est.arma.wge(fcases_s7,p = 21,q=8)
##
## Coefficients of Original polynomial:
## -0.0230 -1.0213 -0.5401 -0.4897 -0.4550 -0.2080 -0.1938 -0.1226 -0.0104 0.1365 0.1375 0.1623 0.1617 0.1532 0.0733 0.1025 0.1675 0.0892 0.1631 0.0571 0.0339
##
## Factor Roots Abs Recip System Freq
## 1-0.8434B+0.9161B^2 0.4603+-0.9379i 0.9571 0.1774
## 1-0.4874B+0.8831B^2 0.2760+-1.0277i 0.9398 0.2082
## 1-1.3847B+0.8822B^2 0.7848+-0.7194i 0.9393 0.1181
## 1-0.9178B 1.0895 0.9178 0.0000
## 1+0.4712B+0.8325B^2 -0.2830+-1.0588i 0.9124 0.2916
## 1-1.5629B+0.7633B^2 1.0238+-0.5118i 0.8737 0.0738
## 1+1.7231B+0.7609B^2 -1.1322+-0.1795i 0.8723 0.4750
## 1+1.5068B+0.7564B^2 -0.9961+-0.5744i 0.8697 0.4168
## 1+1.0733B+0.7475B^2 -0.7179+-0.9069i 0.8646 0.3566
## 1+9e-04B+0.6831B^2 -6e-04+-1.2099i 0.8265 0.2501
## 1+0.4441B+0.2770B^2 -0.8016+-1.7227i 0.5263 0.3193
##
##
#Run ljung test with autocrrelation
plotts.sample.wge(est_fcases_s7p21q8$res,lag.max = 40,arlimits = T)


## $autplt
## [1] 1.000000e+00 -9.575288e-03 8.219057e-03 4.304189e-04 -9.360672e-05
## [6] 8.497172e-03 -5.677494e-03 9.498815e-03 -1.225131e-02 8.556901e-03
## [11] -3.288750e-04 -1.108729e-02 5.068849e-03 -1.187879e-02 -2.071742e-03
## [16] -2.063961e-02 7.330368e-03 -1.551226e-02 -2.717393e-02 5.872504e-03
## [21] -5.540850e-03 1.409232e-04 5.275180e-03 2.800586e-02 1.503545e-02
## [26] 7.670708e-02 4.703620e-03 3.051079e-02 8.746116e-02 1.253057e-02
## [31] -2.237561e-02 -1.960129e-02 5.792155e-02 -4.540360e-02 -3.360992e-02
## [36] -3.756302e-02 -1.671010e-02 -2.542129e-02 -8.742100e-02 -1.373872e-02
## [41] 2.559448e-02
##
## $freq
## [1] 0.001655629 0.003311258 0.004966887 0.006622517 0.008278146 0.009933775
## [7] 0.011589404 0.013245033 0.014900662 0.016556291 0.018211921 0.019867550
## [13] 0.021523179 0.023178808 0.024834437 0.026490066 0.028145695 0.029801325
## [19] 0.031456954 0.033112583 0.034768212 0.036423841 0.038079470 0.039735099
## [25] 0.041390728 0.043046358 0.044701987 0.046357616 0.048013245 0.049668874
## [31] 0.051324503 0.052980132 0.054635762 0.056291391 0.057947020 0.059602649
## [37] 0.061258278 0.062913907 0.064569536 0.066225166 0.067880795 0.069536424
## [43] 0.071192053 0.072847682 0.074503311 0.076158940 0.077814570 0.079470199
## [49] 0.081125828 0.082781457 0.084437086 0.086092715 0.087748344 0.089403974
## [55] 0.091059603 0.092715232 0.094370861 0.096026490 0.097682119 0.099337748
## [61] 0.100993377 0.102649007 0.104304636 0.105960265 0.107615894 0.109271523
## [67] 0.110927152 0.112582781 0.114238411 0.115894040 0.117549669 0.119205298
## [73] 0.120860927 0.122516556 0.124172185 0.125827815 0.127483444 0.129139073
## [79] 0.130794702 0.132450331 0.134105960 0.135761589 0.137417219 0.139072848
## [85] 0.140728477 0.142384106 0.144039735 0.145695364 0.147350993 0.149006623
## [91] 0.150662252 0.152317881 0.153973510 0.155629139 0.157284768 0.158940397
## [97] 0.160596026 0.162251656 0.163907285 0.165562914 0.167218543 0.168874172
## [103] 0.170529801 0.172185430 0.173841060 0.175496689 0.177152318 0.178807947
## [109] 0.180463576 0.182119205 0.183774834 0.185430464 0.187086093 0.188741722
## [115] 0.190397351 0.192052980 0.193708609 0.195364238 0.197019868 0.198675497
## [121] 0.200331126 0.201986755 0.203642384 0.205298013 0.206953642 0.208609272
## [127] 0.210264901 0.211920530 0.213576159 0.215231788 0.216887417 0.218543046
## [133] 0.220198675 0.221854305 0.223509934 0.225165563 0.226821192 0.228476821
## [139] 0.230132450 0.231788079 0.233443709 0.235099338 0.236754967 0.238410596
## [145] 0.240066225 0.241721854 0.243377483 0.245033113 0.246688742 0.248344371
## [151] 0.250000000 0.251655629 0.253311258 0.254966887 0.256622517 0.258278146
## [157] 0.259933775 0.261589404 0.263245033 0.264900662 0.266556291 0.268211921
## [163] 0.269867550 0.271523179 0.273178808 0.274834437 0.276490066 0.278145695
## [169] 0.279801325 0.281456954 0.283112583 0.284768212 0.286423841 0.288079470
## [175] 0.289735099 0.291390728 0.293046358 0.294701987 0.296357616 0.298013245
## [181] 0.299668874 0.301324503 0.302980132 0.304635762 0.306291391 0.307947020
## [187] 0.309602649 0.311258278 0.312913907 0.314569536 0.316225166 0.317880795
## [193] 0.319536424 0.321192053 0.322847682 0.324503311 0.326158940 0.327814570
## [199] 0.329470199 0.331125828 0.332781457 0.334437086 0.336092715 0.337748344
## [205] 0.339403974 0.341059603 0.342715232 0.344370861 0.346026490 0.347682119
## [211] 0.349337748 0.350993377 0.352649007 0.354304636 0.355960265 0.357615894
## [217] 0.359271523 0.360927152 0.362582781 0.364238411 0.365894040 0.367549669
## [223] 0.369205298 0.370860927 0.372516556 0.374172185 0.375827815 0.377483444
## [229] 0.379139073 0.380794702 0.382450331 0.384105960 0.385761589 0.387417219
## [235] 0.389072848 0.390728477 0.392384106 0.394039735 0.395695364 0.397350993
## [241] 0.399006623 0.400662252 0.402317881 0.403973510 0.405629139 0.407284768
## [247] 0.408940397 0.410596026 0.412251656 0.413907285 0.415562914 0.417218543
## [253] 0.418874172 0.420529801 0.422185430 0.423841060 0.425496689 0.427152318
## [259] 0.428807947 0.430463576 0.432119205 0.433774834 0.435430464 0.437086093
## [265] 0.438741722 0.440397351 0.442052980 0.443708609 0.445364238 0.447019868
## [271] 0.448675497 0.450331126 0.451986755 0.453642384 0.455298013 0.456953642
## [277] 0.458609272 0.460264901 0.461920530 0.463576159 0.465231788 0.466887417
## [283] 0.468543046 0.470198675 0.471854305 0.473509934 0.475165563 0.476821192
## [289] 0.478476821 0.480132450 0.481788079 0.483443709 0.485099338 0.486754967
## [295] 0.488410596 0.490066225 0.491721854 0.493377483 0.495033113 0.496688742
## [301] 0.498344371 0.500000000
##
## $db
## [1] -9.77929899 -1.20426742 4.35651332 -2.77132137 1.94562176
## [6] 3.47589405 -4.32021480 -2.99824311 1.87542525 0.02702706
## [11] -2.06334150 -0.05913589 -6.34882872 -11.59816981 -0.01386932
## [16] -11.22227722 1.51759371 -3.72628001 -1.14815354 -0.91395714
## [21] 0.23023594 5.70741305 2.44972064 4.65564010 -1.42897633
## [26] -6.10583322 4.54359438 -0.99058832 -10.55637294 0.72086893
## [31] -1.44106295 -9.43304075 1.31275532 -11.39591927 -4.72922064
## [36] -8.71295307 -3.44390639 -2.86144499 -9.96380529 2.42379345
## [41] -6.86669158 3.38823179 5.41197355 -5.98767292 0.31082562
## [46] 0.32138361 -2.34069485 -16.37172027 3.68770613 -1.88882013
## [51] 3.36131454 -2.35326282 -0.21092350 -1.39252138 -3.31641675
## [56] -4.75558857 -3.88387690 2.16192708 2.67837114 2.52754457
## [61] -0.94126047 -4.14886550 -7.78248303 -1.16576635 -16.13089098
## [66] -0.31253816 3.26408439 1.53069996 3.32543501 -11.05196880
## [71] -0.67921511 -2.34689508 0.13545192 3.16971830 -10.15460275
## [76] 0.34522711 -2.81384391 -4.88267002 2.81634026 -0.68477687
## [81] 3.36388544 -2.60808725 0.78363740 0.49268402 -15.45745049
## [86] -10.61096149 -25.59247826 1.14806125 0.56437221 0.02160886
## [91] 6.53142546 -4.41455996 0.69549975 -4.87210214 -1.77684620
## [96] -3.24653658 -5.05699018 -2.52867663 1.91211209 1.47761228
## [101] -12.77945797 -1.67736090 2.41904606 0.57506859 2.53586890
## [106] -5.33364204 0.39748867 -3.43235991 1.57257615 1.42340150
## [111] 1.12389713 -3.10860127 -0.82261667 -7.75935580 3.67466132
## [116] -14.74636008 -2.51653735 4.74740147 -7.63861288 -3.00882340
## [121] 1.61253873 -6.03672424 1.14828956 1.79007738 -2.47979190
## [126] 1.55099302 -12.37263458 2.64333310 -2.63266819 1.51616676
## [131] -1.14402054 -1.67823563 -1.08036769 3.08557872 0.68443908
## [136] -4.69271070 4.80508323 -0.95089634 -2.37218691 -9.42946269
## [141] -1.02919799 -14.12046406 -4.92582155 -3.35331964 -5.67589905
## [146] -2.43991933 -1.74767030 0.70039017 5.50639892 3.38908844
## [151] 4.95690991 -0.93006008 -1.96522604 -1.55079870 -2.28558265
## [156] -1.28150462 -4.55144991 -4.58890598 0.88203401 -3.76075762
## [161] -0.19775421 -2.75800538 -1.23719655 -4.20810070 2.08525015
## [166] -0.10846805 0.12379997 2.17035256 -1.33618650 1.86003344
## [171] -1.32375387 0.75830027 -5.91967971 1.03970388 1.65357448
## [176] -0.57350129 1.47195129 1.17037194 -7.28359314 -0.70264530
## [181] -6.72345573 -2.69453433 -1.68232503 -0.96826886 2.28102308
## [186] -14.05222749 4.54413215 -1.17255840 -9.15924929 3.91570087
## [191] -1.60187836 2.37716373 2.51564053 -4.60794056 -1.62224114
## [196] 4.74426690 -6.01744204 -2.43749837 1.32386836 -3.71621110
## [201] 0.09561005 -9.94282391 -6.02172854 0.78313274 2.60344383
## [206] 2.06668691 -4.84275872 -14.85272554 -0.70422152 -1.06799506
## [211] -6.30169864 0.98989557 0.51120159 0.35341363 4.88026431
## [216] 0.08373863 -1.18221568 -2.29930343 1.45643548 2.02181927
## [221] -3.17608712 2.14967439 -10.60426437 -0.37748044 -4.81415248
## [226] -8.89212484 1.60253408 -3.98948876 4.52838995 -0.50769321
## [231] 0.99824569 -6.91414267 1.16015958 3.02579936 -4.80165614
## [236] -6.25120486 -6.55125284 -6.80760141 -7.61441607 -1.08317578
## [241] 6.02167827 -9.52141826 0.70156992 1.74330176 -5.59396822
## [246] 5.38227855 -4.92824975 -1.38845055 2.00605359 -3.51850894
## [251] -4.54306750 1.50016400 -7.11688082 -2.30051184 2.70514710
## [256] -18.92963515 -4.22623350 5.42827996 2.32026493 -7.86315042
## [261] 0.21840996 2.10150965 2.11884594 -1.02652032 4.07876184
## [266] 1.45090777 -7.23516742 2.51235330 -9.41439635 2.92038546
## [271] -1.79006825 -2.56083939 1.02440722 -4.97518117 -0.56585593
## [276] -0.82251513 -1.47424713 1.17030786 -15.73910277 -3.16811046
## [281] -0.08004264 -1.49401838 2.58714144 4.15736023 -3.36455266
## [286] 0.64515396 3.81841874 -5.57795474 -5.26282469 -3.11941199
## [291] -1.31727081 -0.95562353 2.18359764 -1.35524703 1.07806579
## [296] -0.16226653 -1.25407842 2.79056025 -4.11538445 -0.19271379
## [301] 1.50718118 -9.32041614
##
## $dbz
## [1] 0.050827449 0.032661218 0.003281459 -0.035869658 -0.082607029
## [6] -0.133897761 -0.185811829 -0.233585390 -0.271851575 -0.295073074
## [11] -0.298166361 -0.277242645 -0.230325145 -0.157869090 -0.062938681
## [16] 0.049015584 0.170721945 0.293851725 0.409816486 0.510467221
## [21] 0.588629754 0.638471990 0.655738369 0.637901943 0.584280815
## [26] 0.496150139 0.376857646 0.231920864 0.069048556 -0.102008210
## [31] -0.269894630 -0.422485718 -0.548136919 -0.637212666 -0.683564455
## [36] -0.685526376 -0.646086756 -0.572173656 -0.473308412 -0.360053372
## [41] -0.242641615 -0.130004802 -0.029234113 0.054604622 0.118417680
## [46] 0.160895699 0.182263540 0.184008694 0.168606538 0.139247847
## [51] 0.099569381 0.053389597 0.004456041 -0.043783804 -0.088373088
## [56] -0.126982764 -0.157985282 -0.180462958 -0.194158496 -0.199382922
## [61] -0.196900069 -0.187806092 -0.173418062 -0.155179333 -0.134582992
## [66] -0.113109990 -0.092176141 -0.073082117 -0.056962360 -0.044731725
## [71] -0.037031801 -0.034181810 -0.036141118 -0.042491589 -0.052447915
## [76] -0.064902541 -0.078508526 -0.091798661 -0.103332737 -0.111857909
## [81] -0.116461356 -0.116691789 -0.112628363 -0.104882626 -0.094529916
## [86] -0.082978553 -0.071795168 -0.062510393 -0.056430347 -0.054476550
## [91] -0.057071906 -0.064084499 -0.074835134 -0.088168784 -0.102583953
## [96] -0.116407250 -0.127993485 -0.135925757 -0.139187330 -0.137279465
## [101] -0.130267458 -0.118749613 -0.103757756 -0.086609361 -0.068737677
## [106] -0.051526445 -0.036170790 -0.023578007 -0.014313367 -0.008588617
## [111] -0.006285527 -0.007003836 -0.010122375 -0.014863592 -0.020354766
## [116] -0.025683212 -0.029946850 -0.032304593 -0.032032082 -0.028586851
## [121] -0.021682888 -0.011368767 0.001902444 0.017227520 0.033248478
## [126] 0.048202486 0.060032930 0.066559650 0.065698068 0.055710639
## [131] 0.035469861 0.004709243 -0.035764683 -0.083931154 -0.136522818
## [136] -0.189144394 -0.236579915 -0.273304457 -0.294171993 -0.295189466
## [141] -0.274229421 -0.231512013 -0.169726117 -0.093753084 -0.010065916
## [146] 0.074048414 0.151282443 0.214996437 0.259742700 0.281622072
## [151] 0.278500063 0.250116919 0.198114904 0.125985329 0.038915086
## [156] -0.056504662 -0.152747199 -0.242013757 -0.317057790 -0.372064635
## [161] -0.403418128 -0.410170323 -0.394087472 -0.359260580 -0.311390021
## [166] -0.256924735 -0.202234492 -0.152937264 -0.113431571 -0.086627159
## [171] -0.073838857 -0.074804444 -0.087797906 -0.109824412 -0.136895307
## [176] -0.164385154 -0.187465750 -0.201594369 -0.203009842 -0.189169873
## [181] -0.159057254 -0.113298974 -0.054078589 0.015133616 0.089972655
## [186] 0.165618222 0.237213947 0.300221092 0.350687227 0.385431727
## [191] 0.402162812 0.399545320 0.377236606 0.335902325 0.277216177
## [196] 0.203839249 0.119366325 0.028219900 -0.064530327 -0.153440995
## [201] -0.233066836 -0.298412194 -0.345413732 -0.371378860 -0.375294147
## [206] -0.357934009 -0.321741420 -0.270505114 -0.208901291 -0.141987198
## [211] -0.074726424 -0.011600580 0.043667770 0.088280174 0.120428846
## [216] 0.139283414 0.144915927 0.138179271 0.120551686 0.093959263
## [221] 0.060589516 0.022711227 -0.017482644 -0.057993023 -0.097082196
## [226] -0.133287204 -0.165386008 -0.192333504 -0.213191636 -0.227079817
## [231] -0.233167622 -0.230721499 -0.219203122 -0.198401772 -0.168570782
## [236] -0.130532309 -0.085717846 -0.036123756 0.015821634 0.067465296
## [241] 0.116184093 0.159653809 0.196100558 0.224507350 0.244754457
## [246] 0.257676947 0.265026330 0.269327321 0.273628027 0.281154881
## [251] 0.294902446 0.317209124 0.349385189 0.391460678 0.442102449
## [256] 0.498715551 0.557704943 0.614843753 0.665682652 0.705942114
## [261] 0.731848519 0.740396933 0.729540778 0.698318243 0.646927042
## [266] 0.576754930 0.490365458 0.391429360 0.284584342 0.175203300
## [271] 0.069056761 -0.028127344 -0.111175307 -0.175986649 -0.219972198
## [276] -0.242321377 -0.244037626 -0.227733128 -0.197230136 -0.157054397
## [281] -0.111914725 -0.066244849 -0.023852496 0.012309884 0.040259773
## [286] 0.059002076 0.068468861 0.069398449 0.063167854 0.051591145
## [291] 0.036697421 0.020505189 0.004813472 -0.008968230 -0.019930997
## [296] -0.027705002 -0.032422319 -0.034612734 -0.035051676 -0.034585855
## [301] -0.033963872 -0.033696276
acf(est_fcases_s7p21q8$res,lag.max = 50)
pacf(est_fcases_s7p21q8$res,lag.max = 60)
ljung.wge(x = est_fcases_s7p21q8$res,K = 24,p = 2,q = 8)
## Obs -0.009575288 0.008219057 0.0004304189 -9.360672e-05 0.008497172 -0.005677494 0.009498815 -0.01225131 0.008556901 -0.000328875 -0.01108729 0.005068849 -0.01187879 -0.002071742 -0.02063961 0.007330368 -0.01551226 -0.02717393 0.005872504 -0.00554085 0.0001409232 0.00527518 0.02800586 0.01503545
## $test
## [1] "Ljung-Box test"
##
## $K
## [1] 24
##
## $chi.square
## [1] 2.139682
##
## $df
## [1] 14
##
## $pval
## [1] 0.9998743
ljung.wge(x = est_fcases_s7p21q8$res,K = 48,p = 2,q = 8)
## Obs -0.009575288 0.008219057 0.0004304189 -9.360672e-05 0.008497172 -0.005677494 0.009498815 -0.01225131 0.008556901 -0.000328875 -0.01108729 0.005068849 -0.01187879 -0.002071742 -0.02063961 0.007330368 -0.01551226 -0.02717393 0.005872504 -0.00554085 0.0001409232 0.00527518 0.02800586 0.01503545 0.07670708 0.00470362 0.03051079 0.08746116 0.01253057 -0.02237561 -0.01960129 0.05792155 -0.0454036 -0.03360992 -0.03756302 -0.0167101 -0.02542129 -0.087421 -0.01373872 0.02559448 -0.01264854 -0.01854353 -0.0665434 0.02314855 0.05067647 -0.05989914 0.02035279 -0.01398838
## $test
## [1] "Ljung-Box test"
##
## $K
## [1] 48
##
## $chi.square
## [1] 31.18086
##
## $df
## [1] 38
##
## $pval
## [1] 0.775425
#Identify Rolling Window ASE for short term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 7,s = 7,phis = est_fcases_s7p21q8$phi,thetas = est_fcases_s7p21q8$theta,trainingSize = 60)
#Identify Rolling Window ASE for long term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 21,s = 7,phis = est_fcases_s7p21q8$phi,thetas = est_fcases_s7p21q8$theta,trainingSize = 60)

Assume it has no seasonality
fcases_d1=artrans.wge(covid$case_count,phi.tr = c(1),lag.max = 40)

pcases_d1=artrans.wge(cases$Case.Count,phi.tr = c(1),lag.max = 40)

#Dicky-Fuller Test shows another d=1 does not belong in the data
adf.test(fcases_d1)
## Warning in adf.test(fcases_d1): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: fcases_d1
## Dickey-Fuller = -11.526, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
#We can see the remaining data is not white noise from the ACF
full_s7=plotts.sample.wge(fcases_d1,lag.max = 50,arlimits = T)

#Use overfit to detect any additional seasonality, none found
factor.wge(phi = c(rep(0,2),1))
##
## Coefficients of Original polynomial:
## 0.0000 0.0000 1.0000
##
## Factor Roots Abs Recip System Freq
## 1+1.0000B+1.0000B^2 -0.5000+-0.8660i 1.0000 0.3333
## 1-1.0000B 1.0000 1.0000 0.0000
##
##
est.ar.wge(fcases_d1,p = 17,type = "burg")[0]
##
## Coefficients of Original polynomial:
## -0.5836 -0.7007 -0.6390 -0.5329 -0.5513 -0.2735 0.0220 0.0778 0.0780 0.1346 0.1723 0.1007 0.1063 0.2291 0.1611 0.0851 0.1106
##
## Factor Roots Abs Recip System Freq
## 1-1.2009B+0.9274B^2 0.6474+-0.8118i 0.9630 0.1429
## 1+0.4521B+0.9201B^2 -0.2457+-1.0132i 0.9592 0.2879
## 1+1.0939B+0.8069B^2 -0.6779+-0.8831i 0.8983 0.3542
## 1-0.8904B 1.1231 0.8904 0.0000
## 1+1.5313B+0.7718B^2 -0.9920+-0.5582i 0.8785 0.4184
## 1+1.7121B+0.7537B^2 -1.1358+-0.1916i 0.8682 0.4734
## 1-1.4665B+0.7446B^2 0.9848+-0.6109i 0.8629 0.0884
## 1-0.5548B+0.7039B^2 0.3941+-1.1249i 0.8390 0.1964
## 1-0.0933B+0.5918B^2 0.0788+-1.2975i 0.7693 0.2403
##
##
## named list()
#Show there is white noise remaining (p=0 so null is rejected)
ljung.wge(fcases_d1,K = 24)$pval
## Obs -0.1615376 -0.3407416 -0.01630825 0.03173191 -0.272202 0.08906849 0.4012604 0.007109842 -0.2423124 0.02006031 0.0242998 -0.2228805 0.03869155 0.3513558 -0.006603022 -0.2096946 0.06250296 -0.0239695 -0.1784947 0.03014485 0.2871098 0.02060267 -0.155077 -0.01105907
## [1] 0
ljung.wge(fcases_d1,K = 48)$pval
## Obs -0.1615376 -0.3407416 -0.01630825 0.03173191 -0.272202 0.08906849 0.4012604 0.007109842 -0.2423124 0.02006031 0.0242998 -0.2228805 0.03869155 0.3513558 -0.006603022 -0.2096946 0.06250296 -0.0239695 -0.1784947 0.03014485 0.2871098 0.02060267 -0.155077 -0.01105907 0.02673451 -0.2309074 0.05145384 0.3487136 0.02987283 -0.2194925 -0.04987516 0.04801155 -0.1662238 0.06290646 0.2665929 0.01054959 -0.1774367 -0.0401461 0.02638368 -0.1197962 0.04881206 0.2276451 -0.02742431 -0.1410507 0.05162234 -0.0320819 -0.1193104 0.03610111
## [1] 0
#Use aic5 to find remaining correlation
acf(fcases_d1,lag.max = 60)
pacf(fcases_d1,lag.max = 60)
#aic5.wge(x = fcases_d1,p = 25:30,q = 10:15,type = 'aic')
#Models based on full data
est_fcases_d1p6q14=est.arma.wge(fcases_d1,p = 6,q=14)
##
## Coefficients of Original polynomial:
## -0.8997 -0.8878 -0.9762 -0.8031 -0.9918 -0.7810
##
## Factor Roots Abs Recip System Freq
## 1-1.2331B+0.9808B^2 0.6286+-0.7902i 0.9904 0.1431
## 1+0.4399B+0.9769B^2 -0.2252+-0.9864i 0.9884 0.2857
## 1+1.6928B+0.8152B^2 -1.0383+-0.3855i 0.9029 0.4434
##
##
#Run ljung test with autocrrelation
plotts.sample.wge(est_fcases_d1p6q14$res,lag.max = 40,arlimits = T)


## $autplt
## [1] 1.0000000000 0.0013083094 -0.0008560196 -0.0007060941 -0.0001362948
## [6] 0.0006523680 -0.0046918922 0.0045626103 0.0016006571 -0.0098654627
## [11] -0.0187965302 0.0210342051 -0.0112466654 0.0150252014 0.0125231684
## [16] -0.0061664781 0.0179894403 0.0684617345 -0.0353518445 0.0231186747
## [21] -0.0127348803 -0.0473077082 0.0222093115 0.0701347085 0.0229771437
## [26] 0.0588875602 -0.0122746166 0.0729060111 0.1249720762 0.0497055270
## [31] -0.0364885749 -0.0832642272 0.0285201266 -0.0194777219 -0.0037059795
## [36] -0.0343991007 -0.0362657349 -0.0440623114 -0.1093781267 -0.0163020552
## [41] 0.0332095800
##
## $freq
## [1] 0.002409639 0.004819277 0.007228916 0.009638554 0.012048193 0.014457831
## [7] 0.016867470 0.019277108 0.021686747 0.024096386 0.026506024 0.028915663
## [13] 0.031325301 0.033734940 0.036144578 0.038554217 0.040963855 0.043373494
## [19] 0.045783133 0.048192771 0.050602410 0.053012048 0.055421687 0.057831325
## [25] 0.060240964 0.062650602 0.065060241 0.067469880 0.069879518 0.072289157
## [31] 0.074698795 0.077108434 0.079518072 0.081927711 0.084337349 0.086746988
## [37] 0.089156627 0.091566265 0.093975904 0.096385542 0.098795181 0.101204819
## [43] 0.103614458 0.106024096 0.108433735 0.110843373 0.113253012 0.115662651
## [49] 0.118072289 0.120481928 0.122891566 0.125301205 0.127710843 0.130120482
## [55] 0.132530120 0.134939759 0.137349398 0.139759036 0.142168675 0.144578313
## [61] 0.146987952 0.149397590 0.151807229 0.154216867 0.156626506 0.159036145
## [67] 0.161445783 0.163855422 0.166265060 0.168674699 0.171084337 0.173493976
## [73] 0.175903614 0.178313253 0.180722892 0.183132530 0.185542169 0.187951807
## [79] 0.190361446 0.192771084 0.195180723 0.197590361 0.200000000 0.202409639
## [85] 0.204819277 0.207228916 0.209638554 0.212048193 0.214457831 0.216867470
## [91] 0.219277108 0.221686747 0.224096386 0.226506024 0.228915663 0.231325301
## [97] 0.233734940 0.236144578 0.238554217 0.240963855 0.243373494 0.245783133
## [103] 0.248192771 0.250602410 0.253012048 0.255421687 0.257831325 0.260240964
## [109] 0.262650602 0.265060241 0.267469880 0.269879518 0.272289157 0.274698795
## [115] 0.277108434 0.279518072 0.281927711 0.284337349 0.286746988 0.289156627
## [121] 0.291566265 0.293975904 0.296385542 0.298795181 0.301204819 0.303614458
## [127] 0.306024096 0.308433735 0.310843373 0.313253012 0.315662651 0.318072289
## [133] 0.320481928 0.322891566 0.325301205 0.327710843 0.330120482 0.332530120
## [139] 0.334939759 0.337349398 0.339759036 0.342168675 0.344578313 0.346987952
## [145] 0.349397590 0.351807229 0.354216867 0.356626506 0.359036145 0.361445783
## [151] 0.363855422 0.366265060 0.368674699 0.371084337 0.373493976 0.375903614
## [157] 0.378313253 0.380722892 0.383132530 0.385542169 0.387951807 0.390361446
## [163] 0.392771084 0.395180723 0.397590361 0.400000000 0.402409639 0.404819277
## [169] 0.407228916 0.409638554 0.412048193 0.414457831 0.416867470 0.419277108
## [175] 0.421686747 0.424096386 0.426506024 0.428915663 0.431325301 0.433734940
## [181] 0.436144578 0.438554217 0.440963855 0.443373494 0.445783133 0.448192771
## [187] 0.450602410 0.453012048 0.455421687 0.457831325 0.460240964 0.462650602
## [193] 0.465060241 0.467469880 0.469879518 0.472289157 0.474698795 0.477108434
## [199] 0.479518072 0.481927711 0.484337349 0.486746988 0.489156627 0.491566265
## [205] 0.493975904 0.496385542 0.498795181
##
## $db
## [1] -5.979200749 4.853218808 1.730262672 2.458077251 -6.537585992
## [6] 1.335814543 -1.357039730 -1.683463469 -6.834339701 -6.291968971
## [11] -14.563072409 -3.729585234 -0.673962095 -3.538504014 4.737728994
## [16] 2.635246097 1.970765879 -5.900146427 4.179737593 -12.133748523
## [21] 2.576546182 -6.375369255 -3.811442484 -4.306877625 -7.352313154
## [26] -14.203698823 -19.441249042 2.524421031 7.512491118 -6.888343576
## [31] 3.314402083 -16.173119179 -8.322717194 0.890566311 3.863824819
## [36] -5.341585084 -0.805469198 -9.101966087 -6.364534637 0.881163819
## [41] 2.352306347 -5.721072681 -25.713951416 -4.252666029 -4.519706222
## [46] 3.056979511 4.740959892 -5.688988308 2.221313400 -3.143611479
## [51] 2.400212525 -0.374154956 -5.405087608 1.225570924 -4.405360152
## [56] 1.771600146 0.040771587 -3.074854601 1.582413830 -5.767742753
## [61] 2.490427471 3.470899716 -7.658136035 -0.779672194 -1.635976876
## [66] -6.007745612 -2.325197083 -0.559304982 -5.323170707 -1.180273286
## [71] 1.117471470 5.626365758 -0.306094627 1.888039401 4.485690891
## [76] -2.885055208 -2.381270067 -7.993699428 0.997303122 -7.893325326
## [81] -0.255793106 -9.001316904 -6.070418449 -7.384868406 3.614028514
## [86] -0.279278934 -1.547772169 3.964184632 -7.486166384 -0.778412250
## [91] 0.452006658 2.191858951 1.504092849 2.620409573 -5.369877309
## [96] -10.423209358 -2.369090781 -4.330658880 -4.199163399 -3.701520540
## [101] -2.793191720 4.650358921 3.510252280 3.661293962 -2.645778785
## [106] -0.786899261 -0.017565062 -1.730780514 -2.674854092 -5.579651405
## [111] 0.495287367 -1.404912475 1.943316573 0.002537396 1.147719616
## [116] -3.528004901 1.534873992 -0.181935698 -2.988733834 0.858486913
## [121] -2.427774594 4.086243096 -2.814760790 -3.654800859 -0.032245263
## [126] -1.412806505 4.186599472 -3.880488314 2.224390869 -3.097296969
## [131] 1.456941334 1.623262811 -0.129285398 -0.788489430 -3.678372355
## [136] -3.667104211 -2.912035882 -1.696235169 -9.461752189 -1.866744217
## [141] 2.319676497 -1.117456269 -11.832258526 1.305206178 -3.795018056
## [146] 1.674775087 1.412355673 4.253674911 0.259852595 -2.731847387
## [151] 4.207346228 2.106721876 -5.902584380 -3.280940605 -8.568020078
## [156] 1.251159482 3.928859062 -3.409267169 -2.106785533 -2.255258274
## [161] 1.356061574 -10.325024422 -12.758670089 -3.772921485 2.231770549
## [166] 0.456644976 2.539031253 -7.992554192 5.118370383 -16.796537063
## [171] 2.771559825 -10.966145056 1.029308125 -10.186852742 1.181352550
## [176] -22.059652657 -1.810194707 4.084812937 -4.773580705 1.302227997
## [181] -5.449041399 3.621791193 -1.987497736 2.537307391 -9.295322137
## [186] 0.341511740 -1.493332887 -0.525931599 0.172385941 -1.962447249
## [191] 1.395873608 -8.708466376 1.130073932 -0.868513141 4.719440804
## [196] -1.499833757 4.096922897 -6.873271384 -4.499052026 -1.520680810
## [201] 2.592660780 -2.530107474 0.889731020 -1.252411949 -0.505980352
## [206] -2.863325161 -2.029537135
##
## $dbz
## [1] 0.3790383552 0.3176212211 0.2216434478 0.1005050465 -0.0331937083
## [6] -0.1646393315 -0.2784983776 -0.3612538707 -0.4037265051 -0.4029835769
## [11] -0.3628693412 -0.2928997180 -0.2059526835 -0.1155832751 -0.0337066105
## [16] 0.0309785921 0.0737998990 0.0942911078 0.0958759464 0.0851154364
## [21] 0.0705275468 0.0610212581 0.0641189871 0.0843136054 0.1219956755
## [26] 0.1732813361 0.2307829414 0.2850503557 0.3262508629 0.3457058914
## [31] 0.3370769233 0.2971628466 0.2263591503 0.1288264964 0.0123528745
## [36] -0.1121842532 -0.2318853032 -0.3334860831 -0.4054565032 -0.4400976371
## [41] -0.4349984087 -0.3933210493 -0.3228145117 -0.2339555834 -0.1378723306
## [46] -0.0446139238 0.0379535141 0.1046134040 0.1527619336 0.1820363887
## [51] 0.1937553568 0.1902873454 0.1744454204 0.1489955848 0.1163531384
## [56] 0.0785125110 0.0372093480 -0.0057429539 -0.0480521970 -0.0866257128
## [61] -0.1174775807 -0.1359829529 -0.1375215080 -0.1184320066 -0.0770631669
## [66] -0.0146133355 0.0645297868 0.1530898763 0.2417717703 0.3204652149
## [71] 0.3795067064 0.4107954903 0.4086756386 0.3705869616 0.2975184297
## [76] 0.1942665766 0.0694247106 -0.0650611287 -0.1949793348 -0.3057105090
## [81] -0.3847071568 -0.4240348292 -0.4221205007 -0.3839885910 -0.3198631196
## [86] -0.2426978770 -0.1655052514 -0.0991804138 -0.0511186959 -0.0246013729
## [91] -0.0187974319 -0.0292497052 -0.0487809044 -0.0687823009 -0.0807901055
## [96] -0.0781235986 -0.0572318365 -0.0183838860 0.0344974912 0.0947791705
## [101] 0.1545190836 0.2059304406 0.2426008388 0.2603161939 0.2574717244
## [106] 0.2351177313 0.1966976472 0.1475235761 0.0940323394 0.0428901065
## [111] 0.0000618988 -0.0299925573 -0.0448301180 -0.0441349519 -0.0294311964
## [116] -0.0035143886 0.0302147045 0.0683338142 0.1077795084 0.1459835976
## [121] 0.1807965670 0.2102761521 0.2324388693 0.2450675816 0.2456447690
## [126] 0.2314471136 0.1998019794 0.1484790325 0.0761746252 -0.0169600100
## [131] -0.1288015466 -0.2548184857 -0.3878177619 -0.5180179225 -0.6336201483
## [136] -0.7220104711 -0.7715687547 -0.7737820761 -0.7250822761 -0.6277655433
## [141] -0.4896407647 -0.3225642422 -0.1404247005 0.0427875987 0.2144161515
## [146] 0.3639691147 0.4834497729 0.5673704515 0.6126210371 0.6183121450
## [151] 0.5856576320 0.5179136152 0.4203508432 0.3002004163 0.1664796120
## [156] 0.0295843368 -0.0994517139 -0.2100584121 -0.2934785700 -0.3440857927
## [161] -0.3602909250 -0.3447191546 -0.3035706077 -0.2453594688 -0.1794021726
## [166] -0.1144212265 -0.0574984468 -0.0134546971 0.0153731166 0.0290277601
## [171] 0.0295686312 0.0205073065 0.0061011128 -0.0094137186 -0.0225361478
## [176] -0.0310304884 -0.0341600905 -0.0325739519 -0.0278827045 -0.0220386016
## [181] -0.0166751446 -0.0125588415 -0.0092707457 -0.0051862641 0.0022320705
## [186] 0.0158718543 0.0382419320 0.0707339577 0.1130525413 0.1629609927
## [191] 0.2164061630 0.2679805601 0.3115979106 0.3412304348 0.3515817252
## [196] 0.3386232541 0.2999758906 0.2351520422 0.1456846811 0.0351608912
## [201] -0.0908429272 -0.2249515436 -0.3583537766 -0.4813869276 -0.5843641877
## [206] -0.6586009627 -0.6975037276
acf(est_fcases_d1p6q14$res,lag.max = 60)
pacf(est_fcases_d1p6q14$res,lag.max = 60)
ljung.wge(x = est_fcases_d1p6q14$res,K = 24,p = 2,q = 8)
## Obs 0.001308309 -0.0008560196 -0.0007060941 -0.0001362948 0.000652368 -0.004691892 0.00456261 0.001600657 -0.009865463 -0.01879653 0.02103421 -0.01124667 0.0150252 0.01252317 -0.006166478 0.01798944 0.06846173 -0.03535184 0.02311867 -0.01273488 -0.04730771 0.02220931 0.07013471 0.02297714
## $test
## [1] "Ljung-Box test"
##
## $K
## [1] 24
##
## $chi.square
## [1] 7.271369
##
## $df
## [1] 14
##
## $pval
## [1] 0.9237437
ljung.wge(x = est_fcases_d1p6q14$res,K = 48,p = 2,q = 8)
## Obs 0.001308309 -0.0008560196 -0.0007060941 -0.0001362948 0.000652368 -0.004691892 0.00456261 0.001600657 -0.009865463 -0.01879653 0.02103421 -0.01124667 0.0150252 0.01252317 -0.006166478 0.01798944 0.06846173 -0.03535184 0.02311867 -0.01273488 -0.04730771 0.02220931 0.07013471 0.02297714 0.05888756 -0.01227462 0.07290601 0.1249721 0.04970553 -0.03648857 -0.08326423 0.02852013 -0.01947772 -0.00370598 -0.0343991 -0.03626573 -0.04406231 -0.1093781 -0.01630206 0.03320958 0.0008057241 -0.01015381 -0.03459925 0.04074889 0.05823959 -0.06546526 0.0008528935 -0.01853162
## $test
## [1] "Ljung-Box test"
##
## $K
## [1] 48
##
## $chi.square
## [1] 36.89734
##
## $df
## [1] 38
##
## $pval
## [1] 0.5203278
#Identify Rolling Window ASE for short term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 7,d = 1,phis = est_fcases_d1p6q14$phi,thetas = est_fcases_d1p6q14$theta,trainingSize = 60)
#Identify Rolling Window ASE for long term forecast
#Rolling_Window_ASE(series = cases$Case.Count,horizon = 21,d = 1,phis = est_fcases_d1p6q14$phi,thetas = est_fcases_d1p6q14$theta,trainingSize = 60)

Generate examples from models selected
#Original Realization
plotts.wge(cases$Case.Count)

#Generated ARIMA(21,0,8)
plotts.wge(gen.aruma.wge(600,phi = est_fcases_s7p21q8$phi,theta = est_fcases_s7p21q8$theta,s = 7,vara = est_fcases_s7p21q8$avar,sn = 25300))


#Generated ARIMA(6,1,14)
plotts.wge(gen.aruma.wge(600,phi = est_fcases_d1p6q14$phi,theta = est_fcases_d1p6q14$theta,d = 1,vara = est_fcases_d1p6q14$avar,sn = 60))


Start Part 2 of Analysis
Read in the data set
covid <- read.csv(text=getURL("https://raw.githubusercontent.com/C-Stewart-GH/Time_Series_Project/main/Raw_Data_Files/merged_data.csv"))
covid$Date=mdy(covid$Date)
str(covid)
## 'data.frame': 416 obs. of 10 variables:
## $ Date : Date, format: "2020-09-14" "2020-09-15" ...
## $ tests_taken : int 34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
## $ case_count : int 3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
## $ retail_and_recreation_percent_change_from_baseline: int -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
## $ grocery_and_pharmacy_percent_change_from_baseline : int -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
## $ parks_percent_change_from_baseline : int 1 7 7 16 6 21 -6 -29 -28 -9 ...
## $ transit_stations_percent_change_from_baseline : int -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
## $ workplaces_percent_change_from_baseline : int -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
## $ residential_percent_change_from_baseline : int 9 10 10 10 9 3 4 12 15 12 ...
## $ vaccine_doses_administered : int 0 0 0 0 0 0 0 0 0 0 ...
summary(covid)
## Date tests_taken case_count
## Min. :2020-09-14 Min. : 0 Min. : 45
## 1st Qu.:2020-12-26 1st Qu.: 61048 1st Qu.: 2325
## Median :2021-04-09 Median : 92026 Median : 4661
## Mean :2021-04-09 Mean : 95723 Mean : 6876
## 3rd Qu.:2021-07-22 3rd Qu.:126984 3rd Qu.:10311
## Max. :2021-11-03 Max. :268222 Max. :28027
## retail_and_recreation_percent_change_from_baseline
## Min. :-78.00
## 1st Qu.:-16.00
## Median : -9.00
## Mean :-11.65
## 3rd Qu.: -6.00
## Max. : 6.00
## grocery_and_pharmacy_percent_change_from_baseline
## Min. :-55.000
## 1st Qu.: -9.000
## Median : -4.000
## Mean : -4.442
## 3rd Qu.: 1.000
## Max. : 29.000
## parks_percent_change_from_baseline
## Min. :-76.000
## 1st Qu.:-16.000
## Median : -3.000
## Mean : -5.724
## 3rd Qu.: 6.000
## Max. : 30.000
## transit_stations_percent_change_from_baseline
## Min. :-68.00
## 1st Qu.:-26.00
## Median :-16.00
## Mean :-18.01
## 3rd Qu.:-10.00
## Max. : 0.00
## workplaces_percent_change_from_baseline
## Min. :-86.00
## 1st Qu.:-33.00
## Median :-29.00
## Mean :-27.25
## 3rd Qu.:-16.75
## Max. : -7.00
## residential_percent_change_from_baseline vaccine_doses_administered
## Min. :-1.000 Min. : 0
## 1st Qu.: 5.000 1st Qu.: 18829
## Median : 7.000 Median : 63698
## Mean : 7.288 Mean : 81305
## 3rd Qu.: 9.000 3rd Qu.:104878
## Max. :29.000 Max. :374014
Visualize full data and create mean mobility
str(covid)
## 'data.frame': 416 obs. of 10 variables:
## $ Date : Date, format: "2020-09-14" "2020-09-15" ...
## $ tests_taken : int 34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
## $ case_count : int 3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
## $ retail_and_recreation_percent_change_from_baseline: int -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
## $ grocery_and_pharmacy_percent_change_from_baseline : int -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
## $ parks_percent_change_from_baseline : int 1 7 7 16 6 21 -6 -29 -28 -9 ...
## $ transit_stations_percent_change_from_baseline : int -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
## $ workplaces_percent_change_from_baseline : int -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
## $ residential_percent_change_from_baseline : int 9 10 10 10 9 3 4 12 15 12 ...
## $ vaccine_doses_administered : int 0 0 0 0 0 0 0 0 0 0 ...
names(covid)
## [1] "Date"
## [2] "tests_taken"
## [3] "case_count"
## [4] "retail_and_recreation_percent_change_from_baseline"
## [5] "grocery_and_pharmacy_percent_change_from_baseline"
## [6] "parks_percent_change_from_baseline"
## [7] "transit_stations_percent_change_from_baseline"
## [8] "workplaces_percent_change_from_baseline"
## [9] "residential_percent_change_from_baseline"
## [10] "vaccine_doses_administered"
covid$mobility_mean=rowMeans(x = covid[,c(4:9)],dims = 1)
plotts.sample.wge(covid$case_count)

## $autplt
## [1] 1.0000000 0.7425282 0.5681884 0.5685943 0.5769823 0.5694251 0.7019362
## [8] 0.7883467 0.6700854 0.5497473 0.5506535 0.5413698 0.5200234 0.6134632
## [15] 0.6862388 0.5791055 0.4755346 0.4793808 0.4504680 0.4346394 0.5112597
## [22] 0.5715589 0.4849685 0.3879385 0.3695535 0.3567548
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 15.3915975 18.4632526 11.2853210 11.0716564 0.3093163 4.9499390
## [7] 2.0109647 0.4500694 -8.8568076 -7.7816920 -16.2112771 -5.1474908
## [13] -4.3890008 -9.3369436 -0.7862864 -3.7681382 -6.2752053 -12.3708249
## [19] -4.4332477 -28.0916503 -5.8310822 -15.3195884 -14.1401708 -14.6743049
## [25] -14.9448720 -21.3642778 -38.2589161 -5.9216012 -1.8099687 -10.4638673
## [31] -4.4354118 -35.4157764 -14.8011192 -6.2561408 -3.8950515 -10.8533207
## [37] -7.6537160 -14.4593527 -11.3330937 -5.9793930 -3.5008067 -8.1084935
## [43] -17.7647573 -7.8158450 -11.6786247 -1.7831609 -0.6907818 -5.6565398
## [49] -2.8314629 -13.8965331 0.2349314 -3.5370873 -10.2305864 -4.0536018
## [55] -5.9246423 0.9755728 -4.4226530 4.5916244 9.9584147 -2.4912398
## [61] 7.2710740 2.5987828 -2.9453740 -1.8352426 -5.5600948 -13.3310388
## [67] -6.8021784 -8.5531231 -5.3218649 -7.2003684 -2.3388024 0.6952226
## [73] -5.8407752 -1.8277963 -1.9053610 -7.1484594 -4.7470266 -8.7136451
## [79] -4.4813375 -18.7421273 -6.7853728 -49.5661075 -12.8856800 -11.1383088
## [85] -2.0006269 -11.1693950 -5.3939753 -5.1994213 -14.8737813 -4.0758832
## [91] -5.5409990 -5.4659455 -5.7376952 -9.5106980 -7.0640107 -10.4334016
## [97] -7.7547565 -12.8322066 -13.9305763 -12.2960066 -10.0585227 -5.6928946
## [103] -2.7778360 -2.2893742 -11.6249579 -6.9351941 -7.1960405 -14.1564481
## [109] -18.4128344 -6.3217552 -6.1256032 -6.2857096 -7.2415358 -5.3985614
## [115] -3.9401621 -2.8056642 1.3802605 -5.3714900 7.5278018 1.8423490
## [121] -0.3541421 -1.5330337 -8.5118989 -4.6759078 -5.5057884 -7.0399737
## [127] -4.4531419 -13.8441388 -2.1971540 -28.0081310 -3.3873168 -10.8405235
## [133] -7.0521061 -25.3589631 -4.5258446 -11.1463496 -8.6616418 -11.9312307
## [139] -13.7477494 -13.7026912 -5.8494544 -7.1039012 -21.2409298 -9.1678052
## [145] -16.2015037 -6.7772933 -11.4192224 -2.6917797 -10.2853156 -10.3603815
## [151] -6.6987701 -13.2684788 -7.0554776 -11.4996202 -12.1916695 -8.7912438
## [157] -15.4502721 -6.2453446 -14.3429745 -10.4618932 -13.3261658 -16.9944583
## [163] -15.3686823 -16.7002621 -22.0137817 -4.8536474 -13.0412320 -8.9138482
## [169] -8.2819848 -9.3758574 -7.8875518 -10.0059583 -10.8398176 -11.6710773
## [175] -12.6553806 -10.2877806 -8.8393494 -9.2518667 -7.8700539 -8.3434222
## [181] -6.6963098 -8.7142459 -7.7126224 -15.9373668 -9.7782580 -6.9771035
## [187] -21.0147620 -9.5746777 -23.7636124 -8.6439000 -8.1495797 -19.8339974
## [193] -12.1937912 -8.6442698 -5.5039774 -7.4264241 -7.2929577 -7.1695303
## [199] -13.3734137 -9.8948865 -9.9663371 -6.7578743 -9.3868384 -9.3159440
## [205] -5.7463010 -19.1656268 -9.8296369 -26.5219166
##
## $dbz
## [1] 12.4980077 12.3324653 12.0557333 11.6665816 11.1633183 10.5438391
## [7] 9.8057220 8.9464053 7.9635137 6.8554399 5.6223686 4.2680384
## [13] 2.8026737 1.2475644 -0.3586597 -1.9537974 -3.4516289 -4.7566327
## [19] -5.7962290 -6.5503790 -7.0498263 -7.3459993 -7.4838913 -7.4956093
## [25] -7.4077784 -7.2493723 -7.0530868 -6.8513006 -6.6708737 -6.5297292
## [31] -6.4357567 -6.3873328 -6.3747405 -6.3822076 -6.3905846 -6.3806134
## [37] -6.3363081 -6.2474794 -6.1103980 -5.9262599 -5.6981243 -5.4276590
## [43] -5.1130146 -4.7486616 -4.3273562 -3.8436396 -3.2975421 -2.6968775
## [49] -2.0571084 -1.3990141 -0.7453869 -0.1180843 0.4638469 0.9849289
## [55] 1.4332221 1.7998843 2.0786064 2.2650905 2.3566492 2.3519568
## [61] 2.2509630 2.0549750 1.7669213 1.3918021 0.9373249 0.4146668
## [67] -0.1607973 -0.7691366 -1.3864194 -1.9867846 -2.5462595 -3.0475669
## [73] -3.4840212 -3.8604197 -4.1902335 -4.4904028 -4.7759700 -5.0562217
## [79] -5.3329251 -5.6005718 -5.8483686 -6.0636397 -6.2359643 -6.3608552
## [85] -6.4416220 -6.4887007 -6.5168890 -6.5417560 -6.5764715 -6.6297058
## [91] -6.7046655 -6.7990719 -6.9059014 -7.0148031 -7.1141041 -7.1931283
## [97] -7.2442694 -7.2640858 -7.2528728 -7.2127036 -7.1445322 -7.0453261
## [103] -6.9062862 -6.7131285 -6.4490586 -6.1001549 -5.6613788 -5.1403628
## [109] -4.5569225 -3.9387394 -3.3156990 -2.7153320 -2.1603810 -1.6682148
## [115] -1.2513294 -0.9182672 -0.6745496 -0.5234461 -0.4665275 -0.5040090
## [121] -0.6349050 -0.8570171 -1.1667695 -1.5589060 -2.0260693 -2.5583137
## [127] -3.1426552 -3.7628456 -4.3996397 -5.0318428 -5.6382680 -6.2003292
## [133] -6.7044889 -7.1435403 -7.5161021 -7.8246069 -8.0728340 -8.2641631
## [139] -8.4011989 -8.4866729 -8.5249411 -8.5232053 -8.4918205 -8.4435692
## [145] -8.3922539 -8.3511538 -8.3317754 -8.3430752 -8.3911199 -8.4790423
## [151] -8.6071408 -8.7730075 -8.9716288 -9.1954579 -9.4345256 -9.6767136
## [157] -9.9083545 -10.1153105 -10.2845552 -10.4060473 -10.4744165 -10.4898737
## [163] -10.4579583 -10.3881786 -10.2920209 -10.1809443 -10.0648276 -9.9510667
## [169] -9.8442975 -9.7466123 -9.6581158 -9.5776785 -9.5037532 -9.4351221
## [175] -9.3714511 -9.3135529 -9.2633203 -9.2233584 -9.1964047 -9.1846540
## [181] -9.1891078 -9.2090465 -9.2417097 -9.2822576 -9.3240820 -9.3595077
## [187] -9.3808573 -9.3817344 -9.3582555 -9.3098959 -9.2396910 -9.1537329
## [193] -9.0601371 -8.9677863 -8.8851550 -8.8194028 -8.7757911 -8.7573878
## [199] -8.7649820 -8.7971427 -8.8503766 -8.9193782 -8.9973873 -9.0766829
## [205] -9.1492319 -9.2074753 -9.2451806 -9.2582295
plotts.sample.wge(covid$tests_taken)

## $autplt
## [1] 1.0000000 0.4389657 0.3875677 0.3685486 0.4752392 0.4390029 0.4628439
## [8] 0.4584686 0.3807932 0.4338508 0.4118061 0.4242590 0.3479843 0.3591513
## [15] 0.3587381 0.3882476 0.3662274 0.3509530 0.2916578 0.2922313 0.3578795
## [22] 0.2864460 0.3168696 0.2423636 0.2888662 0.2181025
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 11.301482768 16.742501527 13.938286669 7.504777383 -0.400126316
## [6] 2.391341544 1.073663371 -6.857810339 1.678387751 0.638385980
## [11] -6.182935039 -3.469259133 -8.723612579 -5.426715232 -1.316160648
## [16] 0.797637990 -5.618760155 -4.127587274 -5.988584416 -6.058339606
## [21] -7.695388765 -2.578776800 -6.820386550 -5.576576412 -4.508218184
## [26] -13.876321507 -3.174791842 -16.732836142 -8.768701185 -3.577321043
## [31] -1.202154668 -5.038512028 -8.331710704 -4.066469401 -4.852897903
## [36] -1.371009223 -34.283467220 -23.779467922 -3.737088080 -5.812902916
## [41] -9.218636437 -0.579846142 -2.748092277 -4.390244359 -3.393223261
## [46] -0.292061649 -4.534397018 -13.770173502 2.405587355 1.210473331
## [51] -9.150274921 -6.865624284 -3.297440451 -18.989750087 -2.442401237
## [56] -1.786787712 -2.646506136 -6.608748724 5.333370671 -0.722509695
## [61] -8.721982527 -3.067603641 -3.913130547 -3.547350197 -5.991583655
## [66] -4.681809451 -14.114927540 -3.176836413 -6.360535874 -0.499462294
## [71] 0.183307045 -2.082160462 1.075049473 0.245116747 -1.768675373
## [76] -6.056625760 -1.316002484 -1.477120281 -3.920164578 6.793413599
## [81] 0.004314842 -6.645020575 -4.919219669 -4.324277485 2.828021178
## [86] -0.333430600 -5.642506320 -1.400377926 -8.215132811 3.392776823
## [91] -7.785385949 -7.275891232 -1.546634350 -11.759421968 -8.578455264
## [96] -1.761168880 0.224506803 -0.150603128 -13.705803799 -6.619692601
## [101] -0.596506069 -4.898663361 -0.293108454 -7.217629556 2.214680664
## [106] -9.300503349 -6.359843900 2.975161673 -2.168245042 -1.949975193
## [111] -3.882536088 -10.949097544 -3.060185856 -1.729569711 -23.959001796
## [116] -4.613753882 -2.769643394 -5.111552083 3.235249654 3.528232631
## [121] -14.236526706 -9.861521007 -6.653801570 -3.123817336 -10.751069548
## [126] 4.104365745 -1.474074947 -8.692513432 -1.517413116 -2.083189487
## [131] 0.282553039 -10.578790204 -7.968846007 -2.603150864 -0.476766421
## [136] -4.945883435 -4.335297028 -5.880510375 -7.728565405 -13.622615583
## [141] -0.171147878 -22.837692732 1.495014077 -1.966990856 -6.072698146
## [146] -4.768052086 -8.848059167 -0.633937164 -6.348319911 -5.897781046
## [151] -4.651051143 -5.826110039 -10.083918946 -7.864396637 1.435736442
## [156] -6.297410926 -11.668116458 -7.582812623 -11.741405252 -17.414356795
## [161] -6.281131357 -2.370400417 -15.243980620 -4.976417827 -7.941595279
## [166] -25.342125839 -2.477548401 -3.832264481 -6.854448428 -1.104286257
## [171] 0.485117435 -10.624120674 -8.815420092 0.172519564 -7.578435629
## [176] -5.189221838 0.280241668 -3.674721947 -5.618911571 -6.132505319
## [181] -4.317429733 -2.250085356 -7.044884748 -5.489149712 0.846110509
## [186] 1.359802470 -8.750868858 -3.966329245 -13.613887995 4.972532577
## [191] 1.267481407 3.533672260 -7.928548779 -6.868175544 -2.893487925
## [196] -4.748188636 -3.529268289 -9.334279299 -7.733091735 -4.448188504
## [201] -0.827648576 -0.715687584 -3.219041616 -3.081507901 -5.250788983
## [206] -8.063543780 0.924605929 -5.903270635
##
## $dbz
## [1] 10.87672478 10.71859138 10.45463892 10.08433601 9.60708180 9.02238869
## [7] 8.33018305 7.53129055 6.62820635 5.62629016 4.53555023 3.37312416
## [13] 2.16627394 0.95493760 -0.20848654 -1.26552826 -2.16572145 -2.88308098
## [19] -3.42359762 -3.81738281 -4.10208744 -4.30931762 -4.45957058 -4.56402637
## [25] -4.62915472 -4.66090982 -4.66687606 -4.65616767 -4.63784998 -4.61895889
## [31] -4.60296306 -4.58908966 -4.57260281 -4.54594354 -4.50052089 -4.42879948
## [37] -4.32618289 -4.19216716 -4.03043960 -3.84797039 -3.65348495 -3.45582873
## [43] -3.26262881 -3.07944538 -2.90942677 -2.75339021 -2.61023030 -2.47756562
## [49] -2.35253458 -2.23263418 -2.11647000 -2.00427749 -1.89810530 -1.80162141
## [55] -1.71958724 -1.65710876 -1.61879294 -1.60791698 -1.62567926 -1.67057326
## [61] -1.73792860 -1.81970207 -1.90466212 -1.97915400 -2.02858997 -2.03961124
## [67] -2.00252518 -1.91330322 -1.77440775 -1.59413283 -1.38477090 -1.16033522
## [73] -0.93455160 -0.71951046 -0.52502001 -0.35849319 -0.22514942 -0.12834916
## [79] -0.06994325 -0.05057415 -0.06990398 -0.12676585 -0.21924574 -0.34470657
## [85] -0.49976734 -0.68025129 -0.88111896 -1.09640762 -1.31920775 -1.54172000
## [91] -1.75544841 -1.95158789 -2.12164280 -2.25825706 -2.35614756 -2.41294241
## [97] -2.42968652 -2.41083330 -2.36368533 -2.29741177 -2.22187343 -2.14648911
## [103] -2.07930321 -2.02631974 -1.99109865 -1.97458267 -1.97513109 -1.98876179
## [109] -2.00962422 -2.03072358 -2.04487538 -2.04579130 -2.02910943 -1.99313570
## [115] -1.93910578 -1.87090911 -1.79437999 -1.71637370 -1.64386220 -1.58321752
## [121] -1.53975382 -1.51751584 -1.51925406 -1.54651180 -1.59975567 -1.67849595
## [127] -1.78136323 -1.90612737 -2.04966671 -2.20791730 -2.37585393 -2.54757059
## [133] -2.71653116 -2.87603890 -3.01991894 -3.14332534 -3.24350159 -3.32028500
## [139] -3.37618920 -3.41602001 -3.44612422 -3.47346862 -3.50476093 -3.54576713
## [145] -3.60089623 -3.67304974 -3.76368627 -3.87302927 -4.00033657 -4.14414884
## [151] -4.30243843 -4.47259417 -4.65120761 -4.83367514 -5.01369963 -5.18286044
## [157] -5.33050734 -5.44427938 -5.51147918 -5.52126555 -5.46718580 -5.34917855
## [163] -5.17419051 -4.95509901 -4.70838906 -4.45146914 -4.20040613 -3.96843732
## [169] -3.76522174 -3.59659671 -3.46459057 -3.36752466 -3.30014774 -3.25385643
## [175] -3.21714884 -3.17651120 -3.11789816 -3.02878341 -2.90044067 -2.72981695
## [181] -2.52032676 -2.28125367 -2.02601231 -1.76992531 -1.52818493 -1.31439096
## [187] -1.13972936 -1.01264896 -0.93882943 -0.92126024 -0.96030884 -1.05371664
## [193] -1.19651450 -1.38090366 -1.59620792 -1.82906803 -2.06409401 -2.28516088
## [199] -2.47736140 -2.62930742 -2.73513211 -2.79545047 -2.81685913 -2.81015260
## [205] -2.78790558 -2.76214139 -2.74254009 -2.73529822
plotts.sample.wge(covid$vaccine_doses_administered)

## $autplt
## [1] 1.0000000 0.8739978 0.7176945 0.6405640 0.6291265 0.6764781 0.8038319
## [8] 0.8976695 0.7846137 0.6382382 0.5697411 0.5636810 0.6139153 0.7380781
## [15] 0.8303145 0.7249350 0.5914640 0.5304595 0.5250483 0.5719471 0.6935498
## [22] 0.7827134 0.6756766 0.5425374 0.4836029 0.4823595
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 19.8031590 16.5776853 8.4412122 2.2692821 -3.7506238 4.6644615
## [7] -11.8620479 -11.8394877 -7.3771724 -8.5171703 -4.6411310 2.2644852
## [13] -2.6237705 3.0870535 -4.0197681 1.4603474 -2.2313672 -16.2964445
## [19] -4.0429167 -5.8135809 -3.6026858 -10.1835512 -18.3845286 -7.9079386
## [25] -4.2292645 -8.7632611 -2.4807396 -6.8808953 -2.9822247 -8.9408405
## [31] -9.3893926 -22.1984069 -27.7860778 -17.4879359 -21.6218563 -11.5544712
## [37] -7.3506140 -8.2727532 -23.7231678 -16.0248719 -17.6932012 -24.9912830
## [43] -13.6342967 -5.1161024 -4.1625455 -3.7397838 -12.0454814 -15.1932008
## [49] -24.2456263 -19.3442044 -26.6466035 -17.6847422 -9.9609037 -5.6279883
## [55] -3.8905548 -7.9359161 -0.1804803 5.2430989 10.8429959 10.0398269
## [61] 3.7482925 1.2430409 -6.2126859 -4.2137135 -8.4144517 -13.0738966
## [67] -15.9059014 -27.8219245 -14.7036111 -11.7152205 -13.7819145 -10.0760627
## [73] -9.4334624 -14.5706632 -10.0971016 -13.4075679 -7.5545256 -21.9267874
## [79] -17.9699735 -33.0857903 -22.7334698 -28.1449051 -15.8630842 -22.0528487
## [85] -10.1148729 -16.1206581 -17.7191448 -21.7006892 -28.8189877 -22.7341323
## [91] -28.8041913 -18.5658677 -20.4065001 -16.7679390 -14.6314233 -15.4111069
## [97] -22.7344409 -15.7265477 -11.2430690 -12.1876173 -13.4147465 -15.6656922
## [103] -11.5672267 -17.3503463 -17.4477962 -11.9631222 -15.6377206 -17.4345442
## [109] -30.5379090 -38.5652278 -11.0609262 -24.2002231 -11.4564842 -16.3469576
## [115] -19.9062603 -11.1256667 -3.5377852 0.2047136 5.9883934 -3.8936478
## [121] -4.3097116 -40.9866320 -22.9485197 -22.3026175 -19.5211635 -20.5095509
## [127] -18.2959585 -17.8264900 -24.5978152 -24.5249461 -19.4589624 -15.7950286
## [133] -21.6006903 -24.0674711 -17.6157609 -16.5770373 -20.4492716 -35.7070911
## [139] -19.8255067 -16.3578606 -16.3343163 -17.3467215 -50.4725287 -20.0842116
## [145] -21.7248943 -18.8423050 -27.4947222 -15.9169183 -20.4016861 -19.5675077
## [151] -17.7157665 -21.6261069 -19.0791114 -18.9175678 -25.9022328 -15.3688348
## [157] -21.7648147 -24.8539248 -28.0186543 -26.4770252 -15.7006530 -22.7703689
## [163] -24.1471094 -32.6621384 -32.4220683 -14.0896990 -23.9027656 -21.7035386
## [169] -17.5936864 -28.1614025 -22.6763194 -23.6764886 -28.5357625 -14.0264419
## [175] -27.8796759 -14.6932928 -9.4918853 -2.6032371 -3.5233444 -16.7626445
## [181] -14.1350310 -12.2590569 -9.2160757 -22.4641841 -16.5823658 -24.8758840
## [187] -31.4532246 -21.6759018 -23.0952986 -20.2193044 -14.0913243 -27.5939366
## [193] -26.3169394 -26.1495841 -39.5512932 -16.8872991 -14.5149737 -16.0831032
## [199] -12.5278486 -23.8445423 -23.1621474 -24.1838867 -20.9260170 -21.7691310
## [205] -16.7109886 -17.3245034 -15.7383890 -27.5638586
##
## $dbz
## [1] 13.1746181 12.9955964 12.6963481 12.2756110 11.7317517 11.0629552
## [7] 10.2675690 9.3447123 8.2953394 7.1240462 5.8420217 4.4715035
## [13] 3.0514794 1.6423237 0.3231856 -0.8260467 -1.7566566 -2.4744796
## [19] -3.0310044 -3.4902959 -3.9001045 -4.2813949 -4.6327468 -4.9421118
## [25] -5.2000988 -5.4097165 -5.5888271 -5.7653950 -5.9693546 -6.2252509
## [31] -6.5474260 -6.9373525 -7.3821968 -7.8545417 -8.3146178 -8.7171903
## [37] -9.0234694 -9.2133289 -9.2891690 -9.2666807 -9.1572646 -8.9521241
## [43] -8.6169908 -8.1036120 -7.3771054 -6.4431602 -5.3523257 -4.1788348
## [49] -2.9945020 -1.8544365 -0.7950997 0.1617934 1.0044324 1.7270440
## [55] 2.3272703 2.8045226 3.1589897 3.3910521 3.5009381 3.4885243
## [61] 3.3532212 3.0939126 2.7089380 2.1961214 1.5528716 0.7764017
## [67] -0.1358298 -1.1852841 -2.3708000 -3.6858448 -5.1138641 -6.6212086
## [73] -8.1487191 -9.6079236 -10.8948302 -11.9300720 -12.7028789 -13.2734210
## [79] -13.7291471 -14.1391271 -14.5349160 -14.9134011 -15.2500593 -15.5162598
## [85] -15.6955635 -15.7923533 -15.8288799 -15.8341523 -15.8322489 -15.8352223
## [91] -15.8415113 -15.8387672 -15.8098423 -15.7404125 -15.6257223 -15.4735058
## [97] -15.3016267 -15.1315840 -14.9804039 -14.8527280 -14.7336828 -14.5835592
## [103] -14.3384969 -13.9248767 -13.2900478 -12.4327790 -11.4062556 -10.2911019
## [109] -9.1643255 -8.0836303 -7.0861791 -6.1934918 -5.4169219 -4.7618147
## [115] -4.2302274 -3.8225896 -3.5386817 -3.3782014 -3.3410893 -3.4277126
## [121] -3.6389635 -3.9762964 -4.4417078 -5.0376359 -5.7667279 -6.6313643
## [127] -7.6327372 -8.7691161 -10.0326838 -11.4040565 -12.8437677 -14.2820619
## [133] -15.6149092 -16.7233431 -17.5250727 -18.0233629 -18.2981235 -18.4493071
## [139] -18.5510563 -18.6399358 -18.7236094 -18.7946903 -18.8430125 -18.8638733
## [145] -18.8612200 -18.8462063 -18.8330734 -18.8347626 -18.8598476 -18.9112270
## [151] -18.9863252 -19.0783711 -19.1783691 -19.2773627 -19.3684691 -19.4480598
## [157] -19.5155321 -19.5714358 -19.6141259 -19.6355079 -19.6169057 -19.5269484
## [163] -19.3244819 -18.9691870 -18.4380388 -17.7384076 -16.9077627 -16.0003687
## [169] -15.0712354 -14.1659806 -13.3178804 -12.5492148 -11.8740208 -11.3007245
## [175] -10.8341602 -10.4769666 -10.2304948 -10.0953701 -10.0718106 -10.1597663
## [181] -10.3589072 -10.6684547 -11.0868150 -11.6109367 -12.2352659 -12.9501371
## [187] -13.7394610 -14.5777896 -15.4275036 -16.2381982 -16.9517688 -17.5157635
## [193] -17.9013415 -18.1143869 -18.1905525 -18.1783925 -18.1229192 -18.0570290
## [199] -18.0002487 -17.9612170 -17.9411325 -17.9368849 -17.9434826 -17.9557328
## [205] -17.9692353 -17.9807956 -17.9884143 -17.9910577
plotts.sample.wge(covid$retail_and_recreation_percent_change_from_baseline)

## $autplt
## [1] 1.0000000 0.6983174 0.5868280 0.5095025 0.4666940 0.4459558 0.4622844
## [8] 0.4912353 0.4217998 0.3916000 0.3759614 0.3762750 0.4004297 0.4046370
## [15] 0.4153277 0.3814206 0.3774123 0.3610891 0.3448507 0.3479561 0.3513856
## [22] 0.3808831 0.3743044 0.3414351 0.3215593 0.3175316
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 18.37283971 9.36706876 7.70415501 9.35121559 1.90413861
## [6] 7.70726735 -6.54338792 3.49863057 6.18353052 2.49014183
## [11] 4.40450490 3.26856751 -6.31916458 2.06941390 -0.25851934
## [16] 2.19179334 4.79782479 3.01483806 2.15211045 2.03574805
## [21] -3.22581164 2.45973555 -0.86087505 1.87118628 2.11256564
## [26] 4.23767975 -4.52401881 -9.57609423 -7.32316519 -0.71563805
## [31] -0.60870599 3.07167438 2.42417546 -0.05708961 1.68808336
## [36] -0.23261918 -2.31254842 -6.58152518 -5.58007894 -0.68518727
## [41] -0.66766507 -1.54214733 -9.35312630 -6.61307420 0.93739896
## [46] 1.91075212 0.19060731 -1.22771314 -2.47997926 -10.03670141
## [51] -9.09376483 -9.80336785 -7.33657542 -0.68898736 -0.06300741
## [56] 2.55559683 2.51345338 -4.12752465 4.94568994 -4.34038974
## [61] 1.91026473 -2.29485579 1.66133597 -3.42661775 -6.13934835
## [66] -14.52807439 -2.76231778 -3.09359386 -8.13631626 0.92042640
## [71] -0.81184856 -0.91218853 -2.52286869 -0.48613201 -3.05808270
## [76] -3.98702150 -13.64096000 -4.11549841 -5.38316220 -12.37720862
## [81] -7.04232288 -11.35809615 -3.31756162 -3.10906774 -7.31097981
## [86] -13.40219560 -4.58793738 -5.91688253 -10.65056319 -17.56659826
## [91] -5.27916952 -16.32582910 -4.20330572 -4.86005978 -7.13138023
## [96] -9.72321835 -4.13561362 -5.38828436 -5.81459257 -2.52326138
## [101] -3.57376100 -5.92333027 -3.62016034 -3.42778763 -3.48482886
## [106] -7.66275532 -13.38190272 -12.90081369 -9.63946529 -13.25402736
## [111] -11.66476282 -4.85875464 -0.92637276 -0.72684937 -5.26932552
## [116] -7.24116777 -20.36857727 0.56805373 0.48607391 -3.93769670
## [121] -10.50132257 -10.16264005 -11.51912545 -10.58277120 -9.40788437
## [126] -8.59176370 -5.43688229 -2.74837328 0.06498268 0.18200760
## [131] -2.79411721 -7.83604702 -9.38332993 -22.96634701 -27.30847892
## [136] -17.81641101 -13.01545761 -2.56400034 -4.80416686 -5.80148130
## [141] -7.37652914 -9.07906915 -6.52134671 -6.03449469 -5.50832430
## [146] -3.84292231 -7.54405424 -7.14347196 -8.39252762 -9.92597198
## [151] -10.50410120 -13.05320945 -16.67966754 -6.33725683 -3.51609523
## [156] -15.60404613 -6.75550373 -4.95296889 -4.28758353 -7.20350796
## [161] -2.95879620 -10.88165318 -8.47075545 -23.01099535 -9.66002295
## [166] -17.40753639 -18.30570661 -9.70160702 -19.41804135 -4.00117919
## [171] -3.42241452 -3.44485668 -5.55612827 -0.40570966 -3.06585908
## [176] -3.97499607 -2.69554910 -11.59661505 -10.38409343 -14.52519458
## [181] -10.01753091 -8.14674164 -3.38508893 -3.39898129 -3.06382905
## [186] -3.52903079 -2.50098926 -4.92390430 -9.07116809 -8.46876508
## [191] -11.45289725 -17.55253463 -9.32017821 -10.98104665 -13.55311306
## [196] -5.36245765 -5.21677875 -11.71467812 -5.57847859 -2.45550505
## [201] -4.62797576 -9.45211666 -6.42201399 -5.16389493 -5.63762207
## [206] -7.24831446 -10.76509440 -45.55631953
##
## $dbz
## [1] 11.38914925 11.23202239 10.97089913 10.60715179 10.14321876 9.58320714
## [7] 8.93378112 8.20538523 7.41376995 6.58156536 5.73921528 4.92401004
## [13] 4.17574146 3.52864323 3.00217907 2.59577658 2.29114556 2.06064970
## [19] 1.87659552 1.71735102 1.56939468 1.42645132 1.28722900 1.15287173
## [25] 1.02480185 0.90331273 0.78702336 0.67308247 0.55784770 0.43771551
## [31] 0.30983747 0.17257660 0.02567206 -0.12984223 -0.29188371 -0.45764506
## [37] -0.62391894 -0.78736419 -0.94467461 -1.09263241 -1.22805118 -1.34763703
## [43] -1.44782383 -1.52466477 -1.57388231 -1.59117250 -1.57281188 -1.51651444
## [49] -1.42235849 -1.29350750 -1.13645848 -0.96068892 -0.77777735 -0.60023395
## [55] -0.44031897 -0.30905529 -0.21552222 -0.16641636 -0.16581329 -0.21505883
## [61] -0.31274569 -0.45477471 -0.63454701 -0.84337128 -1.07117882 -1.30759303
## [67] -1.54328403 -1.77137695 -1.98855265 -2.19548630 -2.39645269 -2.59820631
## [73] -2.80846320 -3.03436295 -3.28119112 -3.55149221 -3.84459135 -4.15650061
## [79] -4.48019399 -4.80625116 -5.12384955 -5.42200643 -5.69085561 -5.92265826
## [85] -6.11228048 -6.25705320 -6.35618563 -6.41008742 -6.41995881 -6.38783460
## [91] -6.31701397 -6.21260203 -6.08182690 -5.93389879 -5.77937815 -5.62920230
## [97] -5.49359823 -5.38107428 -5.29759214 -5.24593860 -5.22528516 -5.23095198
## [103] -5.25446603 -5.28408786 -5.30601445 -5.30635948 -5.27371015 -5.20164509
## [109] -5.09034566 -4.94663905 -4.78245154 -4.61230501 -4.45072594 -4.31020554
## [115] -4.19993624 -4.12524151 -4.08750408 -4.08443323 -4.11060208 -4.15826320
## [121] -4.21846965 -4.28246730 -4.34319326 -4.39657656 -4.44228856 -4.48370400
## [127] -4.52707679 -4.58017726 -4.65075017 -4.74510704 -4.86703612 -5.01709482
## [133] -5.19229875 -5.38623705 -5.58968171 -5.79175753 -5.98163628 -6.15050243
## [139] -6.29329627 -6.40965218 -6.50365553 -6.58247563 -6.65433540 -6.72642608
## [145] -6.80325690 -6.88570852 -6.97088745 -7.05279092 -7.12372069 -7.17624468
## [151] -7.20528912 -7.20976510 -7.19317221 -7.16294658 -7.12877501 -7.10040356
## [157] -7.08548577 -7.08782924 -7.10620652 -7.13383474 -7.15870249 -7.16501654
## [163] -7.13595174 -7.05743600 -6.92197504 -6.73104449 -6.49496674 -6.23038795
## [169] -5.95657732 -5.69198452 -5.45190479 -5.24736733 -5.08494107 -4.96707879
## [175] -4.89272891 -4.85808304 -4.85742250 -4.88405993 -4.93134567 -4.99364554
## [181] -5.06713262 -5.15021483 -5.24347086 -5.34907802 -5.46983765 -5.60798509
## [187] -5.76399276 -5.93556167 -6.11698853 -6.29911306 -6.47005982 -6.61690650
## [193] -6.72814500 -6.79637557 -6.82032517 -6.80535492 -6.76221653 -6.70457355
## [199] -6.64620064 -6.59863925 -6.56967242 -6.56262530 -6.57635078 -6.60577965
## [205] -6.64298500 -6.67872482 -6.70432931 -6.71361244
plotts.sample.wge(covid$grocery_and_pharmacy_percent_change_from_baseline)

## $autplt
## [1] 1.0000000 0.5718666 0.4305810 0.3785319 0.3663851 0.3824575 0.4312192
## [8] 0.5548184 0.4246140 0.3853048 0.3565034 0.3606460 0.4055749 0.4196149
## [15] 0.4525967 0.3931202 0.3714544 0.3381515 0.3342886 0.3607135 0.3832291
## [22] 0.4285594 0.3961949 0.3493541 0.3282081 0.3299540
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 18.773019732 -3.162583574 8.993898242 5.030072262 -0.409756488
## [6] 2.350008203 -4.305990161 1.842758341 -0.757595242 1.351931965
## [11] 1.520386459 3.235717694 -2.842935920 0.265444875 -7.916445346
## [16] 2.019850811 3.007367085 -1.157786686 -3.757999311 -8.838270466
## [21] -9.359000699 1.878852393 -3.366243480 -2.280656155 -3.305577002
## [26] 1.147727986 -5.728775369 0.326235298 -15.974831435 -9.155757653
## [31] -8.711484080 2.908127643 3.021403280 -0.207164545 -1.302762649
## [36] -8.276039888 -8.184938806 -3.666192053 -6.466930205 -2.216289264
## [41] 2.735970060 0.071044747 -0.930164633 -13.824831559 -0.887170569
## [46] -0.950825351 1.130401949 1.181874908 1.201634899 -6.073732224
## [51] -15.184566407 -34.183264565 -11.823836487 -2.007452303 -0.009349916
## [56] 3.995441582 3.202001295 1.115731897 7.175289161 3.067723599
## [61] 4.486275898 1.259239597 2.089702084 -2.042488864 -1.239393522
## [66] -9.239440500 -3.640125269 1.721150915 -7.903932819 -0.920435517
## [71] -0.306173787 -0.014994754 0.119778058 1.401319428 -2.348656198
## [76] -5.376882645 -30.286077786 -4.914288872 -3.226709501 -12.150223720
## [81] -12.021709849 -7.167834481 -1.467119727 -0.989459989 -6.098626642
## [86] -10.843662774 -6.915766477 -3.386845894 -4.327459026 -10.085435505
## [91] -6.015232441 -15.247706911 -4.448077073 -1.834738422 -3.268136719
## [96] -8.162361319 -10.209504555 -3.491446844 -6.382146318 -3.484469234
## [101] -1.997805727 -6.891748357 -1.212934332 0.218359859 -1.278307024
## [106] -1.159807933 -4.909499598 -6.324744163 -8.890319827 -21.965030281
## [111] -10.161023283 -2.429615291 0.717624155 0.936808292 -2.582049102
## [116] -3.703893255 -4.590650800 -2.336692727 4.559930371 -1.292765344
## [121] -6.003050336 -0.983250934 -5.302796644 -10.048680883 -10.877659156
## [126] -6.958936076 -7.886154271 -0.969264605 -0.132859024 1.777886414
## [131] 0.697496399 -5.640497135 -7.718104598 -24.683122902 -26.503391998
## [136] -14.840889512 -8.971879405 -0.177999250 -2.176193382 -8.915555207
## [141] -4.617606655 -12.470213279 -9.707410219 -6.459800892 -6.093582283
## [146] -3.418487120 -5.856590155 -9.840778362 -7.350589431 -12.423019028
## [151] -7.042230462 -9.659772674 -10.068174118 -4.623261152 -4.401595558
## [156] -19.611035861 -9.522602266 -3.741129305 -5.153107967 -8.848913127
## [161] -2.370487525 -4.338499705 -4.219472546 -10.667172189 -11.647133248
## [166] -9.577817709 -9.037534263 -9.357544031 -6.343933453 -2.582156018
## [171] -1.029626126 -2.885439835 -3.459647935 1.001122257 -1.120494045
## [176] -3.634498144 -0.426626053 -2.366274791 -2.188091234 -5.201642273
## [181] -14.565130067 -5.189152572 -0.877973823 -1.197339269 -1.661047839
## [186] -1.384901017 -0.792967788 -3.039622266 -13.206280959 -11.522184642
## [191] -8.080111229 -10.525603897 -9.293773819 -11.580092865 -8.369891339
## [196] -4.186638135 -5.671966996 -11.328209309 -5.080949562 -2.729439181
## [201] -3.413405374 -10.386187422 -8.538628979 -4.493992263 -6.158802397
## [206] -10.966064660 -11.874034461 -14.328734005
##
## $dbz
## [1] 11.06632233 10.89117632 10.59908748 10.18996064 9.66405160 9.02246472
## [7] 8.26796764 7.40628112 6.44803341 5.41150485 4.32593951 3.23425506
## [13] 2.19233241 1.26091909 0.48898519 -0.10406386 -0.53386371 -0.83907289
## [19] -1.06172751 -1.23293496 -1.36842944 -1.47144180 -1.53885579 -1.56754082
## [25] -1.55875525 -1.51954947 -1.46138510 -1.39723286 -1.33863105 -1.29366364
## [31] -1.26612272 -1.25568197 -1.25877226 -1.26986774 -1.28292270 -1.29270102
## [37] -1.29574143 -1.29075643 -1.27838897 -1.26041202 -1.23858472 -1.21343315
## [43] -1.18321570 -1.14330642 -1.08621150 -1.00240089 -0.88201229 -0.71720786
## [49] -0.50459087 -0.24685689 0.04697281 0.36280966 0.68370113 0.99217460
## [55] 1.27210039 1.50983467 1.69471693 1.81913732 1.87839209 1.87048470
## [61] 1.79595985 1.65779683 1.46133985 1.21420096 0.92603629 0.60807723
## [67] 0.27231850 -0.06965030 -0.40802955 -0.73609779 -1.05100109 -1.35373156
## [73] -1.64824271 -1.93994244 -2.23397313 -2.53367545 -2.83950871 -3.14856990
## [79] -3.45476997 -3.74966860 -4.02387746 -4.26878307 -4.47815888 -4.64916128
## [85] -4.78235662 -4.88078158 -4.94841176 -4.98860021 -5.00299138 -4.99120669
## [91] -4.95135081 -4.88116231 -4.77944876 -4.64734469 -4.48897402 -4.31130673
## [97] -4.12328868 -3.93454745 -3.75403609 -3.58888883 -3.44361988 -3.31968883
## [103] -3.21541522 -3.12623836 -3.04534541 -2.96468754 -2.87633560 -2.77399508
## [109] -2.65435934 -2.51793169 -2.36906385 -2.21521189 -2.06566358 -1.93010839
## [115] -1.81737034 -1.73447729 -1.68609776 -1.67429456 -1.69852723 -1.75585885
## [121] -1.84135582 -1.94868942 -2.07093550 -2.20151961 -2.33518081 -2.46876437
## [127] -2.60164557 -2.73566112 -2.87455720 -3.02309396 -3.18601677 -3.36709622
## [133] -3.56838142 -3.78974642 -4.02876527 -4.28092922 -4.54019851 -4.79983935
## [139] -5.05342188 -5.29576867 -5.52359595 -5.73563271 -5.93214859 -6.11401427
## [145] -6.28157537 -6.43368551 -6.56721340 -6.67723659 -6.75797107 -6.80426329
## [151] -6.81322796 -6.78546626 -6.72537902 -6.64041326 -6.53948305 -6.43105608
## [157] -6.32139965 -6.21332000 -6.10556195 -5.99294661 -5.86729095 -5.71908520
## [163] -5.53972296 -5.32380658 -5.07085428 -4.78582999 -4.47834553 -4.16090799
## [169] -3.84687164 -3.54868176 -3.27671000 -3.03870042 -2.83968941 -2.68223110
## [175] -2.56679407 -2.49224508 -2.45637279 -2.45642085 -2.48959839 -2.55352453
## [181] -2.64655353 -2.76792653 -2.91771085 -3.09651392 -3.30499041 -3.54318789
## [187] -3.80979765 -4.10139969 -4.41182659 -4.73182769 -5.04927863 -5.35019272
## [193] -5.62065486 -5.84944433 -6.03063278 -6.16516222 -6.26066348 -6.32952360
## [199] -6.38594342 -6.44295638 -6.51009623 -6.59196139 -6.68764623 -6.79096933
## [205] -6.89151450 -6.97654038 -7.03365895 -7.05380883
plotts.sample.wge(covid$parks_percent_change_from_baseline)

## $autplt
## [1] 1.0000000 0.7440129 0.6495430 0.5132290 0.4732777 0.5043856 0.4955729
## [8] 0.5909207 0.4750409 0.4689025 0.4107807 0.4139621 0.4814162 0.4599183
## [15] 0.5479859 0.4348813 0.4253223 0.3601215 0.3310964 0.3590276 0.3471454
## [22] 0.4491574 0.3600870 0.3781632 0.3265185 0.3046740
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 18.12171161 14.55252244 1.44610879 8.48672266 7.67812514
## [6] 5.32610757 0.69341894 0.76387998 2.07369358 5.49054846
## [11] 4.73787036 3.66478021 0.27713606 0.84219967 -1.19417922
## [16] -6.73299185 -6.20106003 1.39538382 -4.55923976 0.39921518
## [21] -1.66192022 5.43626047 -2.20172063 -3.16862760 -2.90406608
## [26] 1.82865885 3.91274183 -7.15606128 -3.63138131 -1.71356719
## [31] -7.35719780 -5.90979590 -1.68182559 6.21904714 4.38338758
## [36] -3.32559172 -6.29953103 0.56969189 -1.91325996 -12.96920486
## [41] -2.59055407 -4.31952598 -10.26416979 -4.51444975 -3.90923373
## [46] -4.96140909 -2.55151440 -14.51519226 3.43362914 -6.58984320
## [51] 1.96577208 -2.96532014 -1.33631164 -1.49530973 -0.23501415
## [56] -2.88989747 0.07847912 1.52493266 8.52053903 0.39692148
## [61] 4.26167550 -7.42658019 -3.76017270 -9.32775166 -15.78231191
## [66] 1.34864761 -1.83524830 -16.36957208 -3.35476758 -0.18269683
## [71] -8.01693216 -4.19733815 -4.87630530 -12.27744380 -7.35908878
## [76] -0.58408625 -22.73169092 -5.09740830 -5.32930928 -12.53436384
## [81] -3.88366428 -8.50878113 -6.84065761 -6.62417217 -16.77586531
## [86] -6.22424534 -8.65880788 -24.49756954 -23.05317994 -6.69957674
## [91] -10.95525988 -13.70301890 -6.34325843 -0.30807483 -7.08861268
## [96] -13.96739561 -9.28719355 -11.40868923 -13.52954822 -17.45842472
## [101] -7.18686964 -11.02750850 -2.75502773 -2.96481474 -6.87243555
## [106] -8.23729823 -12.64154326 -8.19220636 -19.45310235 -8.88340369
## [111] -7.80231427 -10.10308458 -8.92519066 -8.41052872 -10.46053792
## [116] -7.21075546 -2.62344885 -6.11284198 0.01792471 -1.76790371
## [121] -14.58315409 -9.65196168 -18.27066267 -8.68727754 -4.29533682
## [126] -14.06844833 -12.82855841 -8.61831734 -6.16719328 -12.25596580
## [131] -18.25607865 -6.95043201 -14.05490375 -24.44227521 -11.53280041
## [136] -11.93231050 -10.19704446 -3.47711792 -13.55978802 -6.75241241
## [141] -18.37630282 -9.29057579 -6.59537863 -10.33908843 -11.44724467
## [146] -6.84537381 -6.15044854 -16.93898768 -26.95676352 -20.41191673
## [151] -7.14586252 -16.89146369 -11.12186630 -14.85651980 -16.80475570
## [156] -9.79630063 -10.16427254 -10.71073771 -10.72842943 -12.51664456
## [161] -18.66088418 -13.37822885 -11.77612378 -13.68223005 -3.42102719
## [166] -11.20517360 -19.23976665 -9.98681315 -10.71020992 -11.63039934
## [171] -13.41273676 -12.29877934 -10.32322591 -6.56190072 -4.42073130
## [176] -0.38288564 -5.72482251 7.91583915 -2.28861978 -9.92487674
## [181] -2.93601986 -12.44277077 -6.11365012 -16.67188194 -13.25625975
## [186] -19.05612764 -13.99618638 -27.50865951 -15.78822387 -30.75454992
## [191] -5.79678298 -4.95384818 -10.62292835 -7.46069770 -9.39768530
## [196] -23.53152855 -12.10663300 -6.64665350 -16.24747290 -11.19580269
## [201] -17.50631382 -12.46580405 -8.72416839 -14.66298718 -4.92517562
## [206] -4.85987089 -26.75541638 -18.50828765
##
## $dbz
## [1] 11.77581084 11.61943076 11.35912995 10.99556183 10.52997611
## [6] 9.96461676 9.30332736 8.55243352 7.72196460 6.82721176
## [11] 5.89042607 4.94205525 4.02032410 3.16759124 2.42274241
## [16] 1.81161468 1.34043762 0.99666119 0.75651682 0.59426339
## [21] 0.48847888 0.42408996 0.39135267 0.38360620 0.39515319
## [26] 0.41992488 0.45102639 0.48092079 0.50190336 0.50658280
## [31] 0.48822663 0.44095977 0.35988371 0.24120922 0.08248645
## [36] -0.11700772 -0.35569173 -0.62891106 -0.92803482 -1.23957825
## [41] -1.54469140 -1.81958022 -2.03754406 -2.17300299 -2.20689771
## [46] -2.13154293 -1.95259296 -1.68711351 -1.35895302 -0.99375278
## [51] -0.61535401 -0.24405797 0.10370322 0.41495388 0.67953026
## [56] 0.88948032 1.03861126 1.12219798 1.13683188 1.08038509
## [61] 0.95207289 0.75260457 0.48441628 0.15197257 -0.23789850
## [66] -0.67571201 -1.14921106 -1.64363084 -2.14256884 -2.62960060
## [71] -3.09051816 -3.51567863 -3.90165958 -4.25151574 -4.57347034
## [76] -4.87852338 -5.17778300 -5.48019559 -5.79098667 -6.11081945
## [81] -6.43556447 -6.75662120 -7.06183765 -7.33711832 -7.56869519
## [86] -7.74573848 -7.86263996 -7.92019530 -7.92524458 -7.88896416
## [91] -7.82451557 -7.74484199 -7.66111664 -7.58196953 -7.51336050
## [96] -7.45887061 -7.42019258 -7.39764603 -7.39059125 -7.39765793
## [101] -7.41674950 -7.44483658 -7.47761533 -7.50917409 -7.53187196
## [106] -7.53665980 -7.51402352 -7.45555615 -7.35587617 -7.21432555
## [111] -7.03581210 -6.83043781 -6.61205260 -6.39627279 -6.19857905
## [116] -6.03289616 -5.91076312 -5.84099208 -5.82963374 -5.88007581
## [121] -5.99314860 -6.16716296 -6.39784994 -6.67821299 -6.99834862
## [126] -7.34535091 -7.70348380 -8.05485621 -8.38080831 -8.66403538
## [131] -8.89112246 -9.05478546 -9.15500408 -9.19859192 -9.19741112
## [136] -9.16595613 -9.11909492 -9.07044808 -9.03150293 -9.01131415
## [141] -9.01656734 -9.05181145 -9.11972637 -9.22134444 -9.35617745
## [146] -9.52221942 -9.71581157 -9.93138322 -10.16113277 -10.39479460
## [151] -10.61973668 -10.82169786 -10.98639774 -11.10192758 -11.16128772
## [156] -11.16398089 -11.11564726 -11.02546080 -10.90194320 -10.74840441
## [161] -10.55930636 -10.31885543 -10.00321984 -9.58727016 -9.05459697
## [166] -8.40633938 -7.66350822 -6.86146691 -6.04055663 -5.23810468
## [171] -4.48428221 -3.80133609 -3.20465415 -2.70440205 -2.30706521
## [176] -2.01666054 -1.83559460 -1.76521833 -1.80613476 -1.95829658
## [181] -2.22090198 -2.59206492 -3.06820203 -3.64304741 -4.30619957
## [186] -5.04117212 -5.82317354 -6.61742853 -7.37977772 -8.06189177
## [191] -8.62201573 -9.03763856 -9.31225297 -9.47092040 -9.54787439
## [196] -9.57430304 -9.57162577 -9.55052990 -9.51360948 -9.45943944
## [201] -9.38655413 -9.29630989 -9.19407848 -9.08878140 -8.99128911
## [206] -8.91242448 -8.86117498 -8.84341372
plotts.sample.wge(covid$transit_stations_percent_change_from_baseline)

## $autplt
## [1] 1.0000000 0.8847764 0.7830763 0.7667176 0.7477690 0.7040921 0.7250004
## [8] 0.7661085 0.7090003 0.6598821 0.6631634 0.6605950 0.6462659 0.6670185
## [15] 0.7020334 0.6653437 0.6328281 0.6347468 0.6217774 0.6060633 0.6268151
## [22] 0.6583927 0.6187125 0.5822011 0.5805933 0.5694103
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 21.07275612 4.75478331 0.69948673 10.76643105 -8.77438423
## [6] 8.27918921 -6.81649963 4.16236616 4.63628327 -1.99406315
## [11] 3.83104458 2.67773075 -12.15663163 -3.10649499 -7.68621103
## [16] -0.37674876 3.27068883 0.68352236 -0.66489086 0.70011592
## [21] -9.50587172 1.79764887 -4.44529966 0.43839924 -2.86210369
## [26] 1.50164481 -3.30567221 -15.83676111 -10.62410832 -2.15036161
## [31] -2.54317395 -2.20045109 -1.95555585 -4.41671008 0.07189779
## [36] -3.77222944 -10.14153542 -6.73614575 -11.00240936 -4.00122162
## [41] -5.17833033 -11.22492470 -19.02800005 -6.26616667 0.02541647
## [46] -1.01359622 -2.59710849 -14.93327915 -5.70094749 -5.90603877
## [51] -8.13865734 -11.68482405 -17.24665002 -3.19838728 -9.74672382
## [56] 0.15492232 1.37668597 -1.69994630 2.30038521 4.35330987
## [61] -9.68102609 -6.59812376 -4.00111848 -15.14199281 -13.37246276
## [66] -18.33920600 -6.57634259 -9.53387289 -18.82585290 -3.66254227
## [71] -5.61399516 -3.81994923 -7.94784825 -4.80764351 -6.45805742
## [76] -6.70068904 -12.88710058 -12.54718104 -15.11511024 -14.84342290
## [81] -7.77820053 -14.52039255 -7.92401160 -8.97081362 -8.46804901
## [86] -7.32797177 -10.79299631 -12.96302443 -12.79786623 -13.54780720
## [91] -9.50983355 -25.76307896 -7.77597083 -8.78702877 -7.72426682
## [96] -14.79486428 -12.29910990 -7.84672680 -15.02082488 -11.04460584
## [101] -10.11320675 -15.48941296 -5.70892096 -5.11161042 -4.26012386
## [106] -3.27040060 -16.80646694 -12.38053367 -12.18369436 -15.51410832
## [111] -8.46891666 -16.68240922 -5.66204135 -3.65873533 -7.29537174
## [116] -11.27257385 -8.18932402 -1.47366555 5.52725072 -10.35790857
## [121] -5.92238127 -10.71007212 -11.15823282 -13.51660957 -23.58209243
## [126] -12.55279278 -12.47065041 -9.18483619 -6.12736486 -6.20483607
## [131] -6.39978224 -14.47232921 -19.06199539 -19.95286687 -27.31975824
## [136] -27.87631386 -20.20383044 -10.47473030 -13.81714473 -13.87694121
## [141] -11.40509272 -20.89984255 -15.91132250 -10.97558700 -12.63112330
## [146] -18.29494888 -17.00604099 -16.34852101 -17.23522850 -14.58677314
## [151] -19.65576116 -12.73605164 -18.83826880 -17.61742064 -17.48971490
## [156] -16.46170399 -16.80899163 -19.79841371 -31.22428993 -25.86028591
## [161] -11.63774827 -25.18282913 -15.18165066 -20.86161791 -19.82713888
## [166] -14.92140032 -17.66763984 -13.75504202 -25.22397806 -13.60560015
## [171] -18.24273862 -10.17034786 -14.23385039 -11.33125853 -18.03360329
## [176] -15.95470825 -8.98959468 -3.09544060 -17.51031612 -18.54538324
## [181] -22.20343916 -13.40459974 -10.34921986 -13.71477716 -13.26615237
## [186] -12.94928201 -17.13034642 -18.21173232 -21.18039224 -25.60966537
## [191] -26.16205388 -12.85990634 -18.34263356 -15.12028224 -11.51056294
## [196] -14.01949386 -15.34154644 -14.29001531 -14.44464367 -13.26274610
## [201] -14.81972528 -21.31405720 -26.20751706 -18.62356470 -9.66207686
## [206] -16.94348919 -24.70852062 -17.57038658
##
## $dbz
## [1] 13.25378361 13.07775368 12.78382951 12.37130807 11.83945405
## [6] 11.18783212 10.41687649 9.52884606 8.52938909 7.43000635
## [11] 6.25164763 5.02920101 3.81518777 2.67831472 1.69084986
## [16] 0.90431446 0.32734549 -0.07479736 -0.35832511 -0.57581088
## [21] -0.76294419 -0.93760498 -1.10526293 -1.26574507 -1.41874744
## [26] -1.56694846 -1.71655540 -1.87590189 -2.05314891 -2.25407579
## [31] -2.48056158 -2.72996770 -2.99541109 -3.26683321 -3.53269937
## [36] -3.78202209 -4.00622391 -4.20028639 -4.36280809 -4.49498654
## [41] -4.59893342 -4.67591244 -4.72501919 -4.74262671 -4.72273256
## [46] -4.65819064 -4.54263724 -4.37269226 -4.14981287 -3.88117912
## [51] -3.57930398 -3.26055538 -2.94315240 -2.64525098 -2.38351554
## [56] -2.17228162 -2.02320907 -1.94524364 -1.94471035 -2.02540337
## [61] -2.18858194 -2.43281932 -2.75368737 -3.14330694 -3.58987267
## [66] -4.07738297 -4.58595546 -5.09319265 -5.57690051 -6.01888187
## [71] -6.40866740 -6.74554478 -7.03778414 -7.29935501 -7.54559588
## [76] -7.78940523 -8.03881684 -8.29606795 -8.55790118 -8.81680537
## [81] -9.06294644 -9.28648762 -9.47983489 -9.63921697 -9.76511027
## [86] -9.86139330 -9.93357407 -9.98671208 -10.02364798 -10.04396610
## [91] -10.04390684 -10.01727862 -9.95723921 -9.85856210 -9.71973483
## [96] -9.54414784 -9.33989539 -9.11824311 -8.89129533 -8.66954350
## [101] -8.45980730 -8.26381891 -8.07755712 -7.89146330 -7.69176369
## [106] -7.46307878 -7.19212342 -6.87162058 -6.50302061 -6.09686143
## [111] -5.67069442 -5.24564929 -4.84306465 -4.48212212 -4.17868659
## [116] -3.94507686 -3.79036158 -3.72084840 -3.74055993 -3.85159135
## [121] -4.05430556 -4.34735252 -4.72751385 -5.18938691 -5.72494781
## [126] -6.32308293 -6.96926223 -7.64563276 -8.33187940 -9.00711093
## [131] -9.65265695 -10.25504756 -10.80796951 -11.31217378 -11.77324337
## [136] -12.19819726 -12.59235846 -12.95760475 -13.29244750 -13.59372473
## [141] -13.85917081 -14.08980568 -14.29114270 -14.47273528 -14.64632878
## [146] -14.82339712 -15.01287513 -15.21958894 -15.44354594 -15.68005529
## [151] -15.92059592 -16.15431599 -16.36993805 -16.55765740 -16.71048299
## [156] -16.82454996 -16.89828598 -16.93078013 -16.92003131 -16.86180185
## [161] -16.74960604 -16.57600933 -16.33495792 -16.02439111 -15.64814047
## [166] -15.21634552 -14.74428025 -14.25017481 -13.75289094 -13.27010396
## [171] -12.81723402 -12.40704354 -12.04967859 -11.75293402 -11.52258324
## [176] -11.36267757 -11.27576613 -11.26301290 -11.32419832 -11.45759644
## [181] -11.65971994 -11.92493303 -12.24495489 -12.60832718 -13.00000945
## [186] -13.40139160 -13.79112081 -14.14710188 -14.44967479 -14.68528206
## [191] -14.84928320 -14.94660475 -14.98987536 -14.99593323 -14.98215508
## [196] -14.96369956 -14.95201469 -14.95440749 -14.97428522 -15.01173076
## [201] -15.06420147 -15.12725010 -15.19522947 -15.26196760 -15.32140129
## [206] -15.36814827 -15.39799114 -15.40824571
plotts.sample.wge(covid$workplaces_percent_change_from_baseline)

## $autplt
## [1] 1.00000000 0.44796635 -0.01288400 0.02633470 -0.03157772 -0.18145143
## [7] 0.18280104 0.59257819 0.17737026 -0.21615134 -0.12899263 -0.13549646
## [13] -0.24339479 0.11873042 0.51357580 0.12541975 -0.22990665 -0.12521062
## [19] -0.13258143 -0.23271999 0.12620792 0.51218310 0.12714698 -0.22630753
## [25] -0.11306640 -0.10286350
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 7.06242102 8.65869199 1.79225738 -16.32912737 0.50166223
## [6] 1.89915277 -4.35989604 3.65331325 6.24581602 4.19342188
## [11] 3.18780981 1.22252444 1.73312254 1.53654600 5.12252156
## [16] 7.50974273 4.06825924 -2.22329651 0.03655859 -1.07893693
## [21] -0.49806934 -25.15427724 -11.99945484 1.54112504 4.37053882
## [26] 1.91026186 2.93510327 -9.36837172 0.46337190 2.00279620
## [31] 0.58880390 -4.36022558 -4.26194105 -3.87495061 0.85091904
## [36] 0.30308088 -0.79560396 -21.42788568 -3.23037815 -1.55929723
## [41] -2.32259361 -21.62982080 -10.95732727 -1.77756879 4.09792471
## [46] 1.55696320 1.74442993 -8.26883352 -8.02735157 -1.28587736
## [51] -3.99048721 -7.76905919 -6.69872645 0.80790046 -6.01206349
## [56] 3.66206743 0.27096449 6.53805667 14.52646677 14.21916351
## [61] 3.85306894 -3.30049155 -3.47608764 -13.69816723 -5.40751094
## [66] -7.06113162 -3.72837620 -7.76801007 -7.80593942 -3.96346089
## [71] -3.75811091 0.01849825 -10.86957801 -10.03974614 -9.24331540
## [76] -5.56243484 -19.23671114 -23.15200947 -19.29555243 -8.32132803
## [81] -7.51645676 -12.14204202 -7.67743186 -31.74178913 -3.53505619
## [86] -17.28175444 -9.96200797 -10.47708442 -14.10155331 -15.15491855
## [91] -14.34470430 -11.20240379 -8.73067731 -3.55246964 -16.11761276
## [96] -16.74895173 -9.60191867 -7.33633192 -14.27249013 -15.18147983
## [101] -6.05335186 -9.34182299 -3.48813226 -3.59544092 -10.99215114
## [106] -1.66679361 -9.58798576 -14.39727423 -11.74675201 -7.26946671
## [111] -8.88029325 -10.86419471 -5.52268328 -2.86292467 -9.95572141
## [116] -21.38234053 1.58352700 3.71457029 16.06320393 -2.57944621
## [121] -5.43136617 -9.66264670 -16.23262677 -6.86856777 -33.63813770
## [126] -10.71162684 -5.99934344 -4.97012645 -6.97226796 -5.72884143
## [131] -9.39291191 -3.67014917 -26.13502818 -13.57241430 -7.75911382
## [136] -29.99017213 -21.68504047 -15.11235698 -7.69164048 -13.51013056
## [141] -4.47086703 -21.04059046 -11.37569671 -8.24128417 -6.81955519
## [146] -17.96743839 -13.58556875 -7.17484674 -16.04817852 -12.58331929
## [151] -9.28604189 -21.17971790 -4.37152576 -9.50890876 -22.86847327
## [156] -9.77374669 -7.95140248 -8.42472305 -24.33389517 -17.31506638
## [161] -8.16914668 -14.54536059 -20.44657872 -8.01566226 -11.74488869
## [166] -6.39206913 -12.80723926 -18.96329573 -6.58404635 -8.20378816
## [171] -8.60517404 -27.14068363 -9.58619266 -10.78669041 -10.63747422
## [176] -14.25244443 -9.50593306 5.32762500 -7.73287327 -6.66083014
## [181] -16.03894334 -10.96361976 -5.37487805 -12.18665205 -24.28596367
## [186] -6.80205101 -17.03315716 -7.99172674 -21.58658802 -10.35494516
## [191] -4.68243590 -15.43522906 -10.64829086 -12.05361379 -13.17044965
## [196] -6.78836134 -13.24202446 -10.94283319 -7.25685411 -11.77930691
## [201] -13.95856522 -20.75620249 -9.07400913 -6.21881257 -8.23412856
## [206] -22.68694272 -9.85314923 -22.79718969
##
## $dbz
## [1] 4.27575543 4.23001059 4.15783386 4.06487447 3.95812315
## [6] 3.84498555 3.73217575 3.62461069 3.52455559 3.43125465
## [11] 3.34116051 3.24869867 3.14735819 3.03085242 2.89414181
## [16] 2.73420175 2.55049555 2.34514708 2.12280317 1.89015823
## [21] 1.65511665 1.42562311 1.20830433 1.00719924 0.82292672
## [26] 0.65257277 0.49037431 0.32903349 0.16134392 -0.01820069
## [31] -0.21206335 -0.41875560 -0.63251836 -0.84377805 -1.04054717
## [36] -1.21073583 -1.34489159 -1.43836740 -1.49175232 -1.50890019
## [41] -1.49285753 -1.44087538 -1.34023610 -1.16704242 -0.89027975
## [46] -0.48207023 0.06916503 0.75030103 1.52583806 2.34886665
## [51] 3.17300690 3.95973848 4.68052984 5.31581698 5.85286998
## [56] 6.28368353 6.60329913 6.80860058 6.89749689 6.86838958
## [61] 6.71984160 6.45039355 6.05850097 5.54259325 4.90128598
## [66] 4.13381923 3.24085266 2.22582927 1.09720886 -0.12810869
## [71] -1.42015204 -2.73119642 -3.99481393 -5.13526439 -6.09081956
## [76] -6.84021861 -7.40954547 -7.85157643 -8.21595350 -8.53061773
## [81] -8.79909971 -9.00873678 -9.14395318 -9.19887165 -9.18363361
## [86] -9.12196141 -9.04277338 -8.97117560 -8.92236153 -8.89902852
## [91] -8.89160881 -8.88088919 -8.84311920 -8.75727887 -8.61253906
## [96] -8.41247942 -8.17345105 -7.91754426 -7.66307869 -7.41540511
## [101] -7.15951567 -6.85620794 -6.44616640 -5.86764892 -5.08548285
## [106] -4.11288179 -3.00667249 -1.84133684 -0.68438366 0.41456229
## [111] 1.42365895 2.32442713 3.10711017 3.76716540 4.30294311
## [116] 4.71424822 5.00147951 5.16512562 5.20547698 5.12247000
## [121] 4.91561848 4.58401408 4.12640025 3.54134822 2.82759752
## [126] 1.98467558 1.01399441 -0.07925659 -1.28296690 -2.57325415
## [131] -3.90806609 -5.22165122 -6.42685808 -7.43497718 -8.19179295
## [136] -8.70375306 -9.02712298 -9.23128291 -9.36905827 -9.46800440
## [141] -9.53612617 -9.57234490 -9.57578556 -9.55106827 -9.50899569
## [146] -9.46389955 -9.42984078 -9.41748584 -9.43245449 -9.47510060
## [151] -9.54134626 -9.62416541 -9.71535806 -9.80725450 -9.89397193
## [156] -9.97190529 -10.03931612 -10.09513597 -10.13731297 -10.16113696
## [161] -10.15800887 -10.11514006 -10.01665983 -9.84640602 -9.59206551
## [166] -9.24941322 -8.82483427 -8.33487618 -7.80310828 -7.25585714
## [171] -6.71849334 -6.21313123 -5.75772855 -5.36613572 -5.04861047
## [176] -4.81245541 -4.66259003 -4.60197297 -4.63184509 -4.75178454
## [181] -4.95956855 -5.25083657 -5.61855765 -6.05233871 -6.53769013
## [186] -7.05551045 -7.58224783 -8.09133308 -8.55631022 -8.95536277
## [191] -9.27580431 -9.51645001 -9.68655519 -9.80187967 -9.87984824
## [196] -9.93570047 -9.98046246 -10.02058753 -10.05868309 -10.09474030
## [201] -10.12743577 -10.15522902 -10.17710103 -10.19288332 -10.20321814
## [206] -10.20925892 -10.21225190 -10.21313424
plotts.sample.wge(covid$residential_percent_change_from_baseline)

## $autplt
## [1] 1.00000000 0.60506428 0.28381540 0.25769045 0.22694571 0.18127506
## [7] 0.42684145 0.67222082 0.39051067 0.11514642 0.10670713 0.09032471
## [13] 0.08306564 0.32639794 0.57256582 0.32697503 0.08650950 0.09635481
## [19] 0.08226207 0.06967052 0.30673273 0.55017876 0.31470706 0.08028669
## [25] 0.08853732 0.08644141
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 16.3778740 10.9114585 2.7520869 3.6174364 -1.2386453 5.1380969
## [7] -9.1017222 5.9408238 6.1204484 1.0549557 4.5470144 4.9184079
## [13] -1.6533875 2.2080740 1.7378020 4.3228212 4.4224081 0.6997466
## [19] 0.5580162 1.4369829 -5.1120485 -2.2641882 -5.0648638 1.0139991
## [25] -0.6195190 2.0462611 1.1982441 -10.1621006 -6.9748443 -0.5685575
## [31] -5.4293556 -3.2073763 -2.8654950 -13.7572844 0.9901236 -4.0432531
## [37] -5.1929505 -7.2912122 -15.2805598 -3.2783757 -10.5139938 -11.5872588
## [43] -17.5029264 -4.3306813 1.1862602 -1.4042093 -4.3414281 -11.5891389
## [49] -1.0541733 1.0458701 -5.8859789 -8.4272169 -4.7342544 -4.3788435
## [55] -8.1701348 4.3722944 2.1278009 5.8201526 12.5911126 13.5517056
## [61] -5.7413541 -4.8721425 -3.4123985 -5.1076896 -5.6089282 -16.5854105
## [67] -1.8497855 -12.9367079 -17.6421634 -0.4400242 -3.6544555 -2.2819690
## [73] -8.7718581 -9.3217243 -5.4993003 -3.9773070 -12.2054656 -22.8764215
## [79] -25.2263992 -8.4898883 -10.8483000 -7.4206548 -4.2264391 -12.0749431
## [85] -5.2657286 -11.3971318 -19.0104246 -6.3797482 -13.9634774 -17.4438232
## [91] -17.9195119 -13.2238189 -5.7336983 -1.7181897 -10.3557433 -12.0249564
## [97] -11.6531224 -6.3397268 -15.5340535 -16.1878553 -7.2515603 -7.5227429
## [103] -5.6058040 -6.0904369 -8.1970915 -1.2992570 -11.8688344 -19.8196235
## [109] -10.6809122 -6.3615510 -7.0387904 -10.5656818 -5.6230125 -3.9999735
## [115] -8.6133229 -18.4337345 -5.0844725 2.4772154 13.5562443 -9.3245116
## [121] -7.4471893 -9.1463631 -12.0187035 -10.8315324 -11.7589324 -20.7429618
## [127] -5.4283603 -5.4998712 -3.4902268 -5.9958660 -7.5182334 -3.9498768
## [133] -17.1337027 -12.2974911 -7.0680983 -12.4511535 -18.5338382 -12.8824046
## [139] -7.9118653 -13.7645725 -4.3720303 -20.1070723 -8.9322585 -6.6319805
## [145] -8.2957586 -22.4030101 -13.2268873 -10.7439029 -25.2027162 -13.6701807
## [151] -6.7300977 -16.1129704 -6.5715726 -10.0792304 -20.6910906 -10.1744365
## [157] -11.4714190 -9.6689978 -28.5094447 -13.8455730 -11.3834431 -12.7874390
## [163] -12.8262003 -10.3250335 -11.0013693 -5.0932254 -18.0258942 -19.7562009
## [169] -11.6006735 -7.8957558 -9.0694014 -13.3980379 -7.1301438 -5.5984021
## [175] -12.6131839 -20.0336593 -13.7160746 4.6367653 -9.0887906 -12.0726144
## [181] -31.9855610 -10.6290041 -6.3649174 -8.8331869 -13.0521184 -6.4397074
## [187] -20.7310298 -9.2845866 -18.2558912 -12.5308938 -7.8352234 -14.2379073
## [193] -9.1011572 -12.8870084 -11.8181276 -7.6285363 -13.9201634 -9.7454996
## [199] -6.1827376 -10.4026103 -10.1117223 -17.7831768 -7.8354297 -9.1222443
## [205] -5.7641523 -18.1011122 -11.8702262 -20.7516956
##
## $dbz
## [1] 9.66730178 9.52174976 9.28103068 8.94823581 8.52828275
## [6] 8.02851337 7.45942734 6.83542791 6.17530635 5.50199848
## [11] 4.84103116 4.21729167 3.65052793 3.15109965 2.71803528
## [16] 2.34054854 2.00229322 1.68634980 1.37911301 1.07228902
## [21] 0.76310767 0.45322727 0.14684370 -0.15150840 -0.43895700
## [26] -0.71560536 -0.98482395 -1.25249400 -1.52548673 -1.80982113
## [31] -2.10891362 -2.42221122 -2.74441394 -3.06549086 -3.37170953
## [36] -3.64776161 -3.87962553 -4.05714254 -4.17486457 -4.23013340
## [41] -4.21862753 -4.12916839 -3.94077513 -3.62529472 -3.15723643
## [46] -2.52752869 -1.75267059 -0.87234275 0.06239380 1.00184938
## [51] 1.90532047 2.74307148 3.49502132 4.14835202 4.69522557
## [56] 5.13100531 5.45299966 5.65962233 5.74985355 5.72291151
## [61] 5.57807512 5.31462677 4.93190961 4.42951944 3.80768224
## [66] 3.06790769 2.21405879 1.25402394 0.20216950 -0.91745418
## [71] -2.06786728 -3.19804272 -4.24778232 -5.16165706 -5.90821271
## [76] -6.49159804 -6.94512556 -7.31168389 -7.62522422 -7.90189768
## [81] -8.14064932 -8.32980486 -8.45626702 -8.51395364 -8.50821645
## [86] -8.45475062 -8.37445216 -8.28737467 -8.20828531 -8.14463084
## [91] -8.09657123 -8.05846596 -8.02133117 -7.97583986 -7.91525756
## [96] -7.83746757 -7.74526882 -7.64457444 -7.54076831 -7.43392363
## [101] -7.31381729 -7.15613190 -6.92234062 -6.56673673 -6.05195684
## [106] -5.36699244 -4.53530461 -3.60644400 -2.63848194 -1.68339095
## [111] -0.78063214 0.04291218 0.77027611 1.39138155 1.90057506
## [116] 2.29488434 2.57287125 2.73391343 2.77777826 2.70439801
## [121] 2.51379478 2.20613613 1.78193215 1.24241399 0.59016907
## [126] -0.16985455 -1.02883434 -1.97194067 -2.97567880 -4.00537848
## [131] -5.01461281 -5.94948481 -6.75995632 -7.41538391 -7.91487255
## [136] -8.28411689 -8.56112748 -8.78118097 -8.96847224 -9.13506056
## [141] -9.28421510 -9.41521925 -9.52762953 -9.62383166 -9.70952356
## [146] -9.79251186 -9.88068656 -9.98005827 -10.09342864 -10.21989611
## [151] -10.35515239 -10.49240738 -10.62371319 -10.74138868 -10.83919086
## [156] -10.91290363 -10.96016361 -10.97958145 -10.96944801 -10.92645050
## [161] -10.84484972 -10.71651298 -10.53205287 -10.28303153 -9.96473817
## [166] -9.57861109 -9.13331430 -8.64400035 -8.13012070 -7.61270487
## [171] -7.11200214 -6.64595101 -6.22949387 -5.87450770 -5.59007518
## [176] -5.38287873 -5.25757962 -5.21710628 -5.26281295 -5.39448537
## [181] -5.61017345 -5.90582989 -6.27473942 -6.70675076 -7.18739927
## [186] -7.69716090 -8.21131529 -8.70112740 -9.13701043 -9.49362239
## [191] -9.75546154 -9.92041486 -9.99928608 -10.01159043 -9.97990453
## [196] -9.92517231 -9.86406178 -9.80818768 -9.76448081 -9.73603985
## [201] -9.72305905 -9.72365628 -9.73456836 -9.75174519 -9.77088777
## [206] -9.78795734 -9.79965001 -9.80379918
plotts.sample.wge(covid$mobility_mean)

## $autplt
## [1] 1.0000000 0.7746703 0.6656403 0.6427164 0.6028464 0.5313645 0.5459950
## [8] 0.6161376 0.5065324 0.4744108 0.5103607 0.5114472 0.4819182 0.4871361
## [15] 0.5540000 0.4659353 0.4394488 0.4706877 0.4558524 0.4091453 0.4159285
## [22] 0.4987903 0.4361481 0.4104534 0.4373936 0.4390635
##
## $freq
## [1] 0.002403846 0.004807692 0.007211538 0.009615385 0.012019231 0.014423077
## [7] 0.016826923 0.019230769 0.021634615 0.024038462 0.026442308 0.028846154
## [13] 0.031250000 0.033653846 0.036057692 0.038461538 0.040865385 0.043269231
## [19] 0.045673077 0.048076923 0.050480769 0.052884615 0.055288462 0.057692308
## [25] 0.060096154 0.062500000 0.064903846 0.067307692 0.069711538 0.072115385
## [31] 0.074519231 0.076923077 0.079326923 0.081730769 0.084134615 0.086538462
## [37] 0.088942308 0.091346154 0.093750000 0.096153846 0.098557692 0.100961538
## [43] 0.103365385 0.105769231 0.108173077 0.110576923 0.112980769 0.115384615
## [49] 0.117788462 0.120192308 0.122596154 0.125000000 0.127403846 0.129807692
## [55] 0.132211538 0.134615385 0.137019231 0.139423077 0.141826923 0.144230769
## [61] 0.146634615 0.149038462 0.151442308 0.153846154 0.156250000 0.158653846
## [67] 0.161057692 0.163461538 0.165865385 0.168269231 0.170673077 0.173076923
## [73] 0.175480769 0.177884615 0.180288462 0.182692308 0.185096154 0.187500000
## [79] 0.189903846 0.192307692 0.194711538 0.197115385 0.199519231 0.201923077
## [85] 0.204326923 0.206730769 0.209134615 0.211538462 0.213942308 0.216346154
## [91] 0.218750000 0.221153846 0.223557692 0.225961538 0.228365385 0.230769231
## [97] 0.233173077 0.235576923 0.237980769 0.240384615 0.242788462 0.245192308
## [103] 0.247596154 0.250000000 0.252403846 0.254807692 0.257211538 0.259615385
## [109] 0.262019231 0.264423077 0.266826923 0.269230769 0.271634615 0.274038462
## [115] 0.276442308 0.278846154 0.281250000 0.283653846 0.286057692 0.288461538
## [121] 0.290865385 0.293269231 0.295673077 0.298076923 0.300480769 0.302884615
## [127] 0.305288462 0.307692308 0.310096154 0.312500000 0.314903846 0.317307692
## [133] 0.319711538 0.322115385 0.324519231 0.326923077 0.329326923 0.331730769
## [139] 0.334134615 0.336538462 0.338942308 0.341346154 0.343750000 0.346153846
## [145] 0.348557692 0.350961538 0.353365385 0.355769231 0.358173077 0.360576923
## [151] 0.362980769 0.365384615 0.367788462 0.370192308 0.372596154 0.375000000
## [157] 0.377403846 0.379807692 0.382211538 0.384615385 0.387019231 0.389423077
## [163] 0.391826923 0.394230769 0.396634615 0.399038462 0.401442308 0.403846154
## [169] 0.406250000 0.408653846 0.411057692 0.413461538 0.415865385 0.418269231
## [175] 0.420673077 0.423076923 0.425480769 0.427884615 0.430288462 0.432692308
## [181] 0.435096154 0.437500000 0.439903846 0.442307692 0.444711538 0.447115385
## [187] 0.449519231 0.451923077 0.454326923 0.456730769 0.459134615 0.461538462
## [193] 0.463942308 0.466346154 0.468750000 0.471153846 0.473557692 0.475961538
## [199] 0.478365385 0.480769231 0.483173077 0.485576923 0.487980769 0.490384615
## [205] 0.492788462 0.495192308 0.497596154 0.500000000
##
## $db
## [1] 19.4590744 11.5047220 4.2706220 8.8818733 1.7815863 7.3556251
## [7] -5.6380415 3.3417920 5.5912176 2.9010450 4.9431953 4.2820147
## [13] -5.2351493 2.1008489 -0.1280291 0.5485545 3.2448561 2.3475387
## [19] 0.3210218 1.3707009 -4.2386145 3.4512580 -2.0845859 -2.1833902
## [25] -3.5484753 3.9277790 1.5400911 -7.1316995 -15.1506191 -1.1619671
## [31] -1.6477689 -0.7976408 1.3750036 1.7423299 3.8633798 -2.8165309
## [37] -2.8775211 -3.1470770 -9.3394435 -2.4537467 -5.8429269 -15.7256625
## [43] -11.6043949 -4.3820916 1.3124995 -0.2811343 -3.6999323 -5.6146837
## [49] 0.4121339 -14.6007161 -2.6936006 -8.2923814 -4.8307606 -11.4485852
## [55] -19.5244255 2.8352715 1.1513844 -2.1435576 0.6485969 -0.3094943
## [61] -1.6522891 -2.1939743 0.1580610 -7.3553929 -14.4289766 -9.4970576
## [67] -2.8398500 -7.8338258 -17.9897088 0.4064696 -2.6452502 -5.2538989
## [73] -4.2466983 -3.9317018 -4.7214779 -2.5964379 -19.7222448 -5.6882367
## [79] -6.1676781 -11.3026911 -17.8766979 -9.6370210 -4.5489082 -7.1841838
## [85] -9.3834122 -8.6942216 -12.2237174 -9.6314332 -13.7216924 -19.8712442
## [91] -16.3897091 -29.8342367 -4.7110309 -2.2737520 -5.9998915 -15.6689463
## [97] -11.5278146 -10.7363636 -12.0739523 -7.5648109 -4.5359461 -15.2843799
## [103] -10.8003367 -10.7489697 -4.8532980 -3.7665504 -23.2465290 -9.2900140
## [109] -17.1314533 -11.6684705 -10.2739876 -6.9373562 -3.6740623 -4.4646553
## [115] -7.8954159 -7.8070138 -10.2464384 0.4696415 8.6047512 -4.0616987
## [121] -10.0747589 -6.9161238 -15.0677557 -22.1798995 -13.1923826 -11.5426030
## [127] -7.5308397 -9.0004327 -3.2656152 -2.5428778 -7.2814615 -6.8377400
## [133] -19.1161403 -20.9429643 -19.1415751 -17.9736993 -12.0761565 -4.9020897
## [139] -6.4807408 -9.8277847 -7.7797817 -26.8790598 -7.5430078 -13.0478550
## [145] -11.6595160 -9.4393028 -7.8707698 -11.2727939 -15.1146464 -13.5303325
## [151] -8.7025348 -15.5089793 -10.1745681 -8.8933312 -11.7768012 -20.3364041
## [157] -12.3464690 -8.1116934 -19.5344533 -17.9910712 -8.4011083 -16.5135652
## [163] -11.3471906 -22.8338096 -9.7092358 -11.1331026 -15.3607456 -12.7286150
## [169] -15.7020537 -6.5840216 -9.5009671 -10.9288616 -7.2220952 -3.1103121
## [175] -7.2218142 -17.4022277 -10.5007304 3.8823798 -11.9739824 -9.8879132
## [181] -13.3747191 -10.9961676 -4.1539554 -7.1430599 -10.1004782 -7.9261476
## [187] -10.1852357 -9.3158117 -21.7651756 -16.3998358 -21.8851154 -10.6370617
## [193] -11.9399962 -10.2253670 -13.4935072 -8.1324885 -8.5264885 -8.9493962
## [199] -9.4249928 -7.4101842 -9.8504002 -12.2516917 -12.9930213 -11.6305059
## [205] -5.6913251 -9.6971565 -15.9003756 -29.1984333
##
## $dbz
## [1] 12.20459483 12.04081039 11.76820076 11.38751432 10.90023881
## [6] 10.30912945 9.61901638 8.83797766 7.97893025 7.06154375
## [11] 6.11400895 5.17352664 4.28368460 3.48717780 2.81494234
## [16] 2.27692656 1.86079657 1.53971708 1.28384444 1.06917418
## [21] 0.88114693 0.71389343 0.56712183 0.44239161 0.34000042
## [26] 0.25721642 0.18804704 0.12420486 0.05662173 -0.02311305
## [31] -0.12175933 -0.24395743 -0.39217422 -0.56688504 -0.76682570
## [36] -0.98920084 -1.22979794 -1.48301920 -1.74189754 -1.99820004
## [41] -2.24272849 -2.46588753 -2.65850365 -2.81276259 -2.92304478
## [46] -2.98643941 -3.00283118 -2.97462374 -2.90628992 -2.80394662
## [51] -2.67505390 -2.52821050 -2.37294218 -2.21938576 -2.07783563
## [56] -1.95819020 -1.86937375 -1.81880586 -1.81196157 -1.85203487
## [61] -1.93970202 -2.07298740 -2.24725865 -2.45541266 -2.68834092
## [66] -2.93575647 -3.18739694 -3.43448006 -3.67112048 -3.89531665
## [71] -4.10918224 -4.31833327 -4.53062751 -4.75462530 -4.99812779
## [76] -5.26700539 -5.56436632 -5.89001226 -6.24010798 -6.60704082
## [81] -6.97953678 -7.34319825 -7.68167467 -7.97858934 -8.22005949
## [86] -8.39723098 -8.50796943 -8.55701586 -8.55454232 -8.51372919
## [91] -8.44826924 -8.37049273 -8.29037182 -8.21529698 -8.15033559
## [96] -8.09864443 -8.06174043 -8.03939611 -8.02901144 -8.02444203
## [101] -8.01447469 -7.98148920 -7.90132530 -7.74573089 -7.48830519
## [106] -7.11286961 -6.62049106 -6.03084667 -5.37699187 -4.69691017
## [111] -4.02623533 -3.39429366 -2.82315344 -2.32839586 -1.92049122
## [116] -1.60615279 -1.38942095 -1.27242980 -1.25588592 -1.33930269
## [121] -1.52102324 -1.79804851 -2.16567368 -2.61693550 -3.14189583
## [126] -3.72685298 -4.35370087 -4.99984371 -5.63923846 -6.24506245
## [131] -6.79391444 -7.27037906 -7.66993970 -7.99864730 -8.26968286
## [136] -8.49859911 -8.69929317 -8.88182787 -9.05212175 -9.21291622
## [141] -9.36529098 -9.51010510 -9.64894106 -9.78437162 -9.91961105
## [146] -10.05778886 -10.20114918 -10.35043816 -10.50464186 -10.66112498
## [151] -10.81611981 -10.96542742 -11.10512593 -11.23205185 -11.34385555
## [156] -11.43853542 -11.51350366 -11.56438925 -11.58391798 -11.56131986
## [161] -11.48277506 -11.33330875 -11.10011183 -10.77647906 -10.36484005
## [166] -9.87743809 -9.33432430 -8.75969516 -8.17815430 -7.61202184
## [171] -7.07998817 -6.59683573 -6.17378222 -5.81907397 -5.53860114
## [176] -5.33642336 -5.21516578 -5.17627843 -5.22016215 -5.34616195
## [181] -5.55242060 -5.83557642 -6.19028374 -6.60854295 -7.07886488
## [186] -7.58538850 -8.10724981 -8.61874930 -9.09105351 -9.49596561
## [191] -9.81136562 -10.02647597 -10.14435985 -10.18021013 -10.15640631
## [196] -10.09686020 -10.02275725 -9.95037700 -9.89059184 -9.84931902
## [201] -9.82835067 -9.82625089 -9.83921381 -9.86188593 -9.88818961
## [206] -9.91216447 -9.92879391 -9.93472930
Look at cross correlation of each variable
par(mfrow=c(1,1))
covid_d1=artrans.wge(covid$case_count,1)

covid_d1s7=artrans.wge(covid_d1,c(rep(0,6),1))

Ccf(covid_d1,artrans.wge(covid$tests_taken,c(1)),lag.max = 40) #Differenced Lag 4

Ccf(covid_d1,artrans.wge(covid$vaccine_doses_administered,c(1)),lag.max = 40) #Seasonal trend remaining


Ccf(covid_d1,artrans.wge(artrans.wge(covid$vaccine_doses_administered,c(1)),c(rep(0,6),1)),lag.max = 40) #Diff and Seas Lag 19



Ccf(covid_d1,artrans.wge(covid$retail_and_recreation_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 1


Ccf(covid_d1,artrans.wge(covid$grocery_and_pharmacy_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 1


Ccf(covid_d1,artrans.wge(covid$parks_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Insignificant


Ccf(covid_d1,artrans.wge(covid$transit_stations_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 1


Ccf(covid_d1,artrans.wge(covid$workplaces_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag 0/ Lag 1


Ccf(covid_d1,artrans.wge(covid$residential_percent_change_from_baseline,c(rep(0,6),1)),lag.max = 40) #Lag -1,0,1


Ccf(covid_d1,artrans.wge(covid$mobility_mean,c(rep(0,6),1)),lag.max = 40) #Lag -1



Create VAR Model
#Create first differenced data set and reduce attributes
covid_d1=covid[,2:dim(covid)[2]]
for (i in c(1:(dim(covid)[2]-1))){
covid_d1[,i]=c(NA,artrans.wge(x = covid_d1[,i],1))
}










names(covid_d1)
## [1] "tests_taken"
## [2] "case_count"
## [3] "retail_and_recreation_percent_change_from_baseline"
## [4] "grocery_and_pharmacy_percent_change_from_baseline"
## [5] "parks_percent_change_from_baseline"
## [6] "transit_stations_percent_change_from_baseline"
## [7] "workplaces_percent_change_from_baseline"
## [8] "residential_percent_change_from_baseline"
## [9] "vaccine_doses_administered"
## [10] "mobility_mean"
str(covid)
## 'data.frame': 416 obs. of 11 variables:
## $ Date : Date, format: "2020-09-14" "2020-09-15" ...
## $ tests_taken : int 34926 57352 51106 104858 124061 33404 31019 54382 79339 123081 ...
## $ case_count : int 3970 5342 6026 4047 3422 3827 2466 9853 17820 3392 ...
## $ retail_and_recreation_percent_change_from_baseline: int -17 -15 -15 -16 -16 -16 -17 -21 -22 -17 ...
## $ grocery_and_pharmacy_percent_change_from_baseline : int -12 -9 -9 -11 -9 -6 -10 -15 -15 -10 ...
## $ parks_percent_change_from_baseline : int 1 7 7 16 6 21 -6 -29 -28 -9 ...
## $ transit_stations_percent_change_from_baseline : int -27 -27 -26 -26 -24 -19 -25 -31 -34 -29 ...
## $ workplaces_percent_change_from_baseline : int -33 -34 -33 -34 -32 -14 -16 -36 -39 -33 ...
## $ residential_percent_change_from_baseline : int 9 10 10 10 9 3 4 12 15 12 ...
## $ vaccine_doses_administered : int 0 0 0 0 0 0 0 0 0 0 ...
## $ mobility_mean : num -13.2 -11.3 -11 -10.2 -11 ...
str(covid_d1)
## 'data.frame': 416 obs. of 10 variables:
## $ tests_taken : num NA 22426 -6246 53752 19203 ...
## $ case_count : num NA 1372 684 -1979 -625 ...
## $ retail_and_recreation_percent_change_from_baseline: num NA 2 0 -1 0 0 -1 -4 -1 5 ...
## $ grocery_and_pharmacy_percent_change_from_baseline : num NA 3 0 -2 2 3 -4 -5 0 5 ...
## $ parks_percent_change_from_baseline : num NA 6 0 9 -10 15 -27 -23 1 19 ...
## $ transit_stations_percent_change_from_baseline : num NA 0 1 0 2 5 -6 -6 -3 5 ...
## $ workplaces_percent_change_from_baseline : num NA -1 1 -1 2 18 -2 -20 -3 6 ...
## $ residential_percent_change_from_baseline : num NA 1 0 0 -1 -6 1 8 3 -3 ...
## $ vaccine_doses_administered : num NA 0 0 0 0 0 0 0 0 0 ...
## $ mobility_mean : num NA 1.833 0.333 0.833 -0.833 ...
covid_d1=covid_d1[2:dim(covid_d1)[1],c(1,2,9,10)]
#Create reduced variable covid data set to mob mean, vax, test count, and case count
names(covid)
## [1] "Date"
## [2] "tests_taken"
## [3] "case_count"
## [4] "retail_and_recreation_percent_change_from_baseline"
## [5] "grocery_and_pharmacy_percent_change_from_baseline"
## [6] "parks_percent_change_from_baseline"
## [7] "transit_stations_percent_change_from_baseline"
## [8] "workplaces_percent_change_from_baseline"
## [9] "residential_percent_change_from_baseline"
## [10] "vaccine_doses_administered"
## [11] "mobility_mean"
covid_reduced=covid[,c(2,3,10,11)]
#Test original data set
VARselect(covid_reduced,lag.max = 45,type = 'const')
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 8 8
##
## $criteria
## 1 2 3 4 5
## AIC(n) 6.191644e+01 6.156413e+01 6.138383e+01 6.126674e+01 6.118286e+01
## HQ(n) 6.200029e+01 6.171506e+01 6.160184e+01 6.155182e+01 6.153502e+01
## SC(n) 6.212756e+01 6.194414e+01 6.193274e+01 6.198453e+01 6.206954e+01
## FPE(n) 7.761992e+26 5.457307e+26 4.557331e+26 4.054321e+26 3.728956e+26
## 6 7 8 9 10
## AIC(n) 6.053240e+01 6.022312e+01 5.984215e+01 5.986445e+01 5.986167e+01
## HQ(n) 6.095164e+01 6.070944e+01 6.039555e+01 6.048493e+01 6.054922e+01
## SC(n) 6.158798e+01 6.144759e+01 6.123552e+01 6.142671e+01 6.159282e+01
## FPE(n) 1.946438e+26 1.429295e+26 9.770909e+25 9.999000e+25 9.980802e+25
## 11 12 13 14 15
## AIC(n) 5.988675e+01 5.990158e+01 5.992411e+01 5.992668e+01 5.991314e+01
## HQ(n) 6.064139e+01 6.072330e+01 6.081291e+01 6.088255e+01 6.093609e+01
## SC(n) 6.178679e+01 6.197052e+01 6.216194e+01 6.233340e+01 6.248875e+01
## FPE(n) 1.024636e+26 1.041414e+26 1.066917e+26 1.071729e+26 1.059687e+26
## 16 17 18 19 20
## AIC(n) 5.995070e+01 5.995843e+01 5.998118e+01 6.003426e+01 6.002764e+01
## HQ(n) 6.104073e+01 6.111554e+01 6.120537e+01 6.132552e+01 6.138599e+01
## SC(n) 6.269521e+01 6.287183e+01 6.306348e+01 6.328544e+01 6.344772e+01
## FPE(n) 1.103074e+26 1.114871e+26 1.144276e+26 1.211089e+26 1.208049e+26
## 21 22 23 24 25
## AIC(n) 6.006241e+01 6.001113e+01 6.001879e+01 6.005369e+01 6.010913e+01
## HQ(n) 6.148783e+01 6.150363e+01 6.157837e+01 6.168035e+01 6.180287e+01
## SC(n) 6.365138e+01 6.376900e+01 6.394554e+01 6.414934e+01 6.437367e+01
## FPE(n) 1.256483e+26 1.199686e+26 1.215597e+26 1.266425e+26 1.347491e+26
## 26 27 28 29 30
## AIC(n) 6.013599e+01 6.017135e+01 6.021626e+01 6.025958e+01 6.027745e+01
## HQ(n) 6.189681e+01 6.199925e+01 6.211123e+01 6.222163e+01 6.230659e+01
## SC(n) 6.456943e+01 6.477368e+01 6.498748e+01 6.519969e+01 6.538646e+01
## FPE(n) 1.394189e+26 1.455725e+26 1.535552e+26 1.618304e+26 1.663875e+26
## 31 32 33 34 35
## AIC(n) 6.032199e+01 6.032185e+01 6.034780e+01 6.031458e+01 6.030017e+01
## HQ(n) 6.241820e+01 6.248514e+01 6.257817e+01 6.261203e+01 6.266470e+01
## SC(n) 6.559989e+01 6.576865e+01 6.596348e+01 6.609916e+01 6.625364e+01
## FPE(n) 1.758284e+26 1.778287e+26 1.847592e+26 1.810911e+26 1.810328e+26
## 36 37 38 39 40
## AIC(n) 6.033013e+01 6.035409e+01 6.033039e+01 6.025304e+01 6.024133e+01
## HQ(n) 6.276174e+01 6.285278e+01 6.289615e+01 6.288588e+01 6.294125e+01
## SC(n) 6.645250e+01 6.664535e+01 6.679054e+01 6.688208e+01 6.703927e+01
## FPE(n) 1.893685e+26 1.971016e+26 1.958096e+26 1.845708e+26 1.859980e+26
## 41 42 43 44 45
## AIC(n) 6.021520e+01 6.017131e+01 6.020696e+01 6.018890e+01 6.015658e+01
## HQ(n) 6.298220e+01 6.300539e+01 6.310812e+01 6.315714e+01 6.319189e+01
## SC(n) 6.718203e+01 6.730704e+01 6.751158e+01 6.766241e+01 6.779898e+01
## FPE(n) 1.849788e+26 1.809595e+26 1.919418e+26 1.932174e+26 1.920325e+26
#AIC 8, BIC 8
#Fit based on AIC
fit1a=VAR(covid_reduced,p=8,type="const")
summary(fit1a)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean
## Deterministic variables: const
## Sample size: 408
## Log Likelihood: -14342.058
## Roots of the characteristic polynomial:
## 0.9897 0.9897 0.9873 0.9873 0.9839 0.9839 0.9477 0.9477 0.9271 0.9271 0.9175 0.907 0.907 0.838 0.8085 0.8085 0.8046 0.8046 0.8014 0.8014 0.7476 0.7476 0.7159 0.7159 0.6988 0.6988 0.5805 0.5805 0.4744 0.3942 0.3942 0.2409
## Call:
## VAR(y = covid_reduced, p = 8, type = "const")
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -3.137e-03 5.164e-02 -0.061 0.9516
## case_count.l1 1.492e+00 5.776e-01 2.584 0.0101 *
## vaccine_doses_administered.l1 4.256e-02 7.317e-02 0.582 0.5611
## mobility_mean.l1 5.304e+02 4.544e+02 1.167 0.2438
## tests_taken.l2 -3.610e-02 5.127e-02 -0.704 0.4818
## case_count.l2 8.663e-01 5.944e-01 1.457 0.1458
## vaccine_doses_administered.l2 -2.517e-02 8.319e-02 -0.303 0.7624
## mobility_mean.l2 3.190e+02 5.162e+02 0.618 0.5369
## tests_taken.l3 -9.317e-02 5.091e-02 -1.830 0.0680 .
## case_count.l3 1.166e+00 5.829e-01 2.001 0.0461 *
## vaccine_doses_administered.l3 5.742e-02 8.318e-02 0.690 0.4904
## mobility_mean.l3 8.330e+01 5.154e+02 0.162 0.8717
## tests_taken.l4 1.012e-01 5.024e-02 2.015 0.0446 *
## case_count.l4 -8.671e-01 5.855e-01 -1.481 0.1395
## vaccine_doses_administered.l4 4.444e-02 8.255e-02 0.538 0.5907
## mobility_mean.l4 1.091e+02 5.162e+02 0.211 0.8328
## tests_taken.l5 6.750e-02 4.988e-02 1.353 0.1768
## case_count.l5 2.322e+00 5.840e-01 3.976 8.42e-05 ***
## vaccine_doses_administered.l5 -1.880e-02 8.292e-02 -0.227 0.8208
## mobility_mean.l5 2.668e+02 5.143e+02 0.519 0.6043
## tests_taken.l6 1.100e-01 4.970e-02 2.213 0.0275 *
## case_count.l6 2.352e-01 5.956e-01 0.395 0.6932
## vaccine_doses_administered.l6 -1.305e-01 8.346e-02 -1.564 0.1188
## mobility_mean.l6 -9.257e+01 5.138e+02 -0.180 0.8571
## tests_taken.l7 1.043e-01 4.949e-02 2.107 0.0358 *
## case_count.l7 -3.631e-01 6.015e-01 -0.604 0.5465
## vaccine_doses_administered.l7 1.118e-01 8.391e-02 1.332 0.1837
## mobility_mean.l7 -3.719e+02 5.123e+02 -0.726 0.4684
## tests_taken.l8 -6.073e-04 4.872e-02 -0.012 0.9901
## case_count.l8 3.622e-01 5.961e-01 0.608 0.5439
## vaccine_doses_administered.l8 -3.348e-02 7.492e-02 -0.447 0.6553
## mobility_mean.l8 1.587e+02 4.634e+02 0.343 0.7321
## const 4.214e+04 7.990e+03 5.274 2.26e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 33900 on 375 degrees of freedom
## Multiple R-Squared: 0.5073, Adjusted R-squared: 0.4653
## F-statistic: 12.07 on 32 and 375 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count:
## ===========================================
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.774e-03 4.612e-03 0.385 0.700656
## case_count.l1 3.618e-01 5.158e-02 7.013 1.09e-11 ***
## vaccine_doses_administered.l1 2.933e-02 6.534e-03 4.488 9.56e-06 ***
## mobility_mean.l1 1.197e+02 4.058e+01 2.951 0.003370 **
## tests_taken.l2 7.240e-03 4.579e-03 1.581 0.114665
## case_count.l2 -1.162e-01 5.308e-02 -2.188 0.029254 *
## vaccine_doses_administered.l2 -2.492e-02 7.429e-03 -3.355 0.000875 ***
## mobility_mean.l2 -4.252e+01 4.609e+01 -0.923 0.356847
## tests_taken.l3 9.642e-03 4.546e-03 2.121 0.034597 *
## case_count.l3 7.315e-02 5.205e-02 1.405 0.160757
## vaccine_doses_administered.l3 8.238e-03 7.428e-03 1.109 0.268102
## mobility_mean.l3 -2.112e+00 4.602e+01 -0.046 0.963424
## tests_taken.l4 1.905e-04 4.486e-03 0.042 0.966159
## case_count.l4 8.491e-02 5.229e-02 1.624 0.105220
## vaccine_doses_administered.l4 -9.461e-03 7.372e-03 -1.283 0.200127
## mobility_mean.l4 -1.035e+02 4.610e+01 -2.245 0.025377 *
## tests_taken.l5 -2.349e-03 4.454e-03 -0.527 0.598219
## case_count.l5 -8.734e-02 5.215e-02 -1.675 0.094841 .
## vaccine_doses_administered.l5 9.837e-03 7.404e-03 1.329 0.184816
## mobility_mean.l5 2.678e+01 4.593e+01 0.583 0.560152
## tests_taken.l6 -6.751e-03 4.438e-03 -1.521 0.129033
## case_count.l6 2.758e-01 5.319e-02 5.184 3.55e-07 ***
## vaccine_doses_administered.l6 -8.642e-03 7.453e-03 -1.160 0.246984
## mobility_mean.l6 6.429e+01 4.589e+01 1.401 0.162013
## tests_taken.l7 -9.700e-03 4.419e-03 -2.195 0.028780 *
## case_count.l7 3.075e-01 5.372e-02 5.724 2.13e-08 ***
## vaccine_doses_administered.l7 -2.975e-03 7.493e-03 -0.397 0.691593
## mobility_mean.l7 -2.888e+01 4.575e+01 -0.631 0.528254
## tests_taken.l8 -1.249e-03 4.351e-03 -0.287 0.774187
## case_count.l8 4.530e-02 5.323e-02 0.851 0.395383
## vaccine_doses_administered.l8 -6.028e-03 6.691e-03 -0.901 0.368164
## mobility_mean.l8 -2.616e+01 4.138e+01 -0.632 0.527708
## const 9.067e+02 7.135e+02 1.271 0.204603
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3027 on 375 degrees of freedom
## Multiple R-Squared: 0.7754, Adjusted R-squared: 0.7562
## F-statistic: 40.46 on 32 and 375 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -1.662e-02 3.048e-02 -0.545 0.585907
## case_count.l1 -6.721e-01 3.409e-01 -1.972 0.049381 *
## vaccine_doses_administered.l1 8.276e-01 4.318e-02 19.165 < 2e-16 ***
## mobility_mean.l1 6.432e+01 2.682e+02 0.240 0.810554
## tests_taken.l2 7.574e-05 3.026e-02 0.003 0.998004
## case_count.l2 3.534e-01 3.508e-01 1.007 0.314364
## vaccine_doses_administered.l2 -7.271e-02 4.909e-02 -1.481 0.139455
## mobility_mean.l2 1.019e+03 3.046e+02 3.345 0.000907 ***
## tests_taken.l3 3.699e-03 3.004e-02 0.123 0.902066
## case_count.l3 -2.823e-01 3.440e-01 -0.821 0.412306
## vaccine_doses_administered.l3 -5.348e-02 4.909e-02 -1.089 0.276637
## mobility_mean.l3 -5.471e+02 3.041e+02 -1.799 0.072864 .
## tests_taken.l4 -2.309e-02 2.965e-02 -0.779 0.436577
## case_count.l4 -1.774e-01 3.455e-01 -0.513 0.608016
## vaccine_doses_administered.l4 8.927e-02 4.872e-02 1.832 0.067674 .
## mobility_mean.l4 4.063e+02 3.046e+02 1.334 0.183111
## tests_taken.l5 9.500e-03 2.944e-02 0.323 0.747060
## case_count.l5 1.560e-01 3.447e-01 0.453 0.651146
## vaccine_doses_administered.l5 -1.011e-01 4.893e-02 -2.067 0.039448 *
## mobility_mean.l5 -2.820e+02 3.035e+02 -0.929 0.353391
## tests_taken.l6 -1.101e-03 2.933e-02 -0.038 0.970074
## case_count.l6 -3.010e-01 3.515e-01 -0.856 0.392351
## vaccine_doses_administered.l6 1.475e-01 4.925e-02 2.995 0.002929 **
## mobility_mean.l6 -9.938e+01 3.032e+02 -0.328 0.743300
## tests_taken.l7 3.212e-02 2.920e-02 1.100 0.272187
## case_count.l7 6.726e-01 3.550e-01 1.895 0.058919 .
## vaccine_doses_administered.l7 6.985e-01 4.952e-02 14.106 < 2e-16 ***
## mobility_mean.l7 -8.367e+02 3.023e+02 -2.767 0.005930 **
## tests_taken.l8 -1.684e-04 2.875e-02 -0.006 0.995331
## case_count.l8 7.902e-02 3.518e-01 0.225 0.822399
## vaccine_doses_administered.l8 -5.657e-01 4.422e-02 -12.794 < 2e-16 ***
## mobility_mean.l8 -7.876e+01 2.735e+02 -0.288 0.773501
## const -1.215e+02 4.715e+03 -0.026 0.979459
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 20000 on 375 degrees of freedom
## Multiple R-Squared: 0.9407, Adjusted R-squared: 0.9357
## F-statistic: 186 on 32 and 375 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 3.178e-06 5.728e-06 0.555 0.579372
## case_count.l1 -8.567e-05 6.407e-05 -1.337 0.181955
## vaccine_doses_administered.l1 2.013e-05 8.116e-06 2.481 0.013543 *
## mobility_mean.l1 6.107e-01 5.040e-02 12.119 < 2e-16 ***
## tests_taken.l2 -1.326e-06 5.687e-06 -0.233 0.815740
## case_count.l2 -5.911e-05 6.592e-05 -0.897 0.370450
## vaccine_doses_administered.l2 -2.629e-05 9.227e-06 -2.849 0.004624 **
## mobility_mean.l2 1.196e-01 5.725e-02 2.089 0.037377 *
## tests_taken.l3 5.108e-06 5.647e-06 0.905 0.366277
## case_count.l3 -9.533e-05 6.465e-05 -1.475 0.141185
## vaccine_doses_administered.l3 1.228e-05 9.226e-06 1.331 0.183997
## mobility_mean.l3 1.028e-02 5.716e-02 0.180 0.857393
## tests_taken.l4 -1.272e-05 5.572e-06 -2.282 0.023026 *
## case_count.l4 4.180e-05 6.494e-05 0.644 0.520144
## vaccine_doses_administered.l4 -1.943e-05 9.156e-06 -2.122 0.034464 *
## mobility_mean.l4 8.696e-02 5.725e-02 1.519 0.129670
## tests_taken.l5 -3.722e-06 5.532e-06 -0.673 0.501498
## case_count.l5 2.191e-05 6.477e-05 0.338 0.735418
## vaccine_doses_administered.l5 1.814e-05 9.196e-06 1.972 0.049335 *
## mobility_mean.l5 -1.084e-01 5.704e-02 -1.900 0.058167 .
## tests_taken.l6 2.740e-06 5.512e-06 0.497 0.619356
## case_count.l6 -1.102e-04 6.606e-05 -1.669 0.096045 .
## vaccine_doses_administered.l6 -6.472e-06 9.257e-06 -0.699 0.484907
## mobility_mean.l6 7.966e-02 5.699e-02 1.398 0.163019
## tests_taken.l7 -1.282e-06 5.489e-06 -0.234 0.815400
## case_count.l7 9.192e-05 6.672e-05 1.378 0.169084
## vaccine_doses_administered.l7 -1.842e-05 9.306e-06 -1.979 0.048551 *
## mobility_mean.l7 2.692e-01 5.682e-02 4.738 3.07e-06 ***
## tests_taken.l8 4.387e-06 5.404e-06 0.812 0.417440
## case_count.l8 1.171e-04 6.612e-05 1.770 0.077463 .
## vaccine_doses_administered.l8 2.016e-05 8.310e-06 2.426 0.015721 *
## mobility_mean.l8 -1.970e-01 5.139e-02 -3.833 0.000148 ***
## const -3.717e-01 8.862e-01 -0.419 0.675169
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.76 on 375 degrees of freedom
## Multiple R-Squared: 0.7433, Adjusted R-squared: 0.7214
## F-statistic: 33.93 on 32 and 375 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1148992753 1679248.8 25719223
## case_count 1679249 9163047.4 4474245
## vaccine_doses_administered 25719223 4474245.1 400159322
## mobility_mean -1283 843.3 16233
## mobility_mean
## tests_taken -1283.34
## case_count 843.29
## vaccine_doses_administered 16232.89
## mobility_mean 14.13
##
## Correlation matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1.00000 0.01637 0.03793
## case_count 0.01637 1.00000 0.07389
## vaccine_doses_administered 0.03793 0.07389 1.00000
## mobility_mean -0.01007 0.07410 0.21584
## mobility_mean
## tests_taken -0.01007
## case_count 0.07410
## vaccine_doses_administered 0.21584
## mobility_mean 1.00000
preds=predict(fit1a,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced)[1],1),covid_reduced$case_count, type = "l")
lines(seq((dim(covid_reduced)[1]-20),dim(covid_reduced)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced$case_count,21), type = "l")
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit1a = mean((tail(covid_reduced$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2)
short_ASE_fit1a
## [1] 3110599
short_ASE_fit1a^.5
## [1] 1763.689
#7 Day RMSE of 1763.7 which is much lower than the 2981 from our ARIMA(6,1,14) model
#Maybe try to look up rolling window version
long_ASE_fit1a = mean((tail(covid_reduced$case_count,21)-preds$fcst$case_count[,1])^2)
long_ASE_fit1a
## [1] 1759871
long_ASE_fit1a^.5
## [1] 1326.601
#RMSE of 1326.6 which is much lower than the 3806 from our ARIMA(6,1,14) model
#Maybe try to look up rolling window version
#Fit based on BIC
#Same
#Test just a seasonal data set
VARselect(covid_reduced,lag.max = 25,type = 'const',season = 7)
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 2 8
##
## $criteria
## 1 2 3 4 5
## AIC(n) 6.060979e+01 6.040078e+01 6.028869e+01 6.019487e+01 6.010890e+01
## HQ(n) 6.078681e+01 6.064217e+01 6.059445e+01 6.056500e+01 6.054341e+01
## SC(n) 6.105640e+01 6.100979e+01 6.106010e+01 6.112868e+01 6.120512e+01
## FPE(n) 2.101473e+26 1.705257e+26 1.524673e+26 1.388464e+26 1.274524e+26
## 6 7 8 9 10
## AIC(n) 5.978701e+01 5.970747e+01 5.947442e+01 5.949180e+01 5.951194e+01
## HQ(n) 6.028589e+01 6.027072e+01 6.010203e+01 6.018379e+01 6.026830e+01
## SC(n) 6.104563e+01 6.112849e+01 6.105784e+01 6.123763e+01 6.142017e+01
## FPE(n) 9.241645e+25 8.540049e+25 6.769682e+25 6.894675e+25 7.042658e+25
## 11 12 13 14 15
## AIC(n) 5.954056e+01 5.954482e+01 5.957640e+01 5.960675e+01 5.960202e+01
## HQ(n) 6.036128e+01 6.042992e+01 6.052587e+01 6.062059e+01 6.068023e+01
## SC(n) 6.161119e+01 6.177786e+01 6.197184e+01 6.216459e+01 6.232226e+01
## FPE(n) 7.256565e+25 7.298778e+25 7.546337e+25 7.794777e+25 7.776078e+25
## 16 17 18 19 20
## AIC(n) 5.963388e+01 5.964254e+01 5.966629e+01 5.970882e+01 5.969266e+01
## HQ(n) 6.077647e+01 6.084949e+01 6.093761e+01 6.104451e+01 6.109273e+01
## SC(n) 6.251653e+01 6.268758e+01 6.287373e+01 6.307866e+01 6.322491e+01
## FPE(n) 8.048998e+25 8.143003e+25 8.366270e+25 8.761863e+25 8.656536e+25
## 21 22 23 24 25
## AIC(n) 5.973521e+01 5.970227e+01 5.971505e+01 5.975114e+01 5.979909e+01
## HQ(n) 6.119965e+01 6.123107e+01 6.130823e+01 6.140868e+01 6.152101e+01
## SC(n) 6.342987e+01 6.355932e+01 6.373451e+01 6.393300e+01 6.414335e+01
## FPE(n) 9.073343e+25 8.822468e+25 8.984112e+25 9.368864e+25 9.891819e+25
#AIC 8, BIC 2
#Fit based on AIC
fit2a=VAR(covid_reduced,p=8,type="const",season = 7)
summary(fit2a)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean
## Deterministic variables: const
## Sample size: 408
## Log Likelihood: -14281.152
## Roots of the characteristic polynomial:
## 0.9892 0.9892 0.9737 0.9737 0.9485 0.9485 0.9186 0.8907 0.8907 0.8787 0.8787 0.8424 0.8424 0.839 0.793 0.793 0.7566 0.7566 0.7383 0.7383 0.738 0.738 0.6698 0.6567 0.6567 0.6407 0.6407 0.6215 0.6215 0.6105 0.6105 0.03927
## Call:
## VAR(y = covid_reduced, p = 8, type = "const", season = 7L)
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -1.286e-03 5.207e-02 -0.025 0.9803
## case_count.l1 1.406e+00 6.105e-01 2.303 0.0219 *
## vaccine_doses_administered.l1 7.124e-02 8.116e-02 0.878 0.3806
## mobility_mean.l1 3.037e+02 4.949e+02 0.614 0.5397
## tests_taken.l2 -3.312e-02 5.176e-02 -0.640 0.5226
## case_count.l2 6.297e-01 6.309e-01 0.998 0.3189
## vaccine_doses_administered.l2 -8.621e-02 1.009e-01 -0.854 0.3934
## mobility_mean.l2 5.465e+02 6.029e+02 0.906 0.3653
## tests_taken.l3 -9.207e-02 5.149e-02 -1.788 0.0746 .
## case_count.l3 1.189e+00 6.187e-01 1.922 0.0554 .
## vaccine_doses_administered.l3 8.163e-02 1.001e-01 0.816 0.4151
## mobility_mean.l3 2.638e+02 6.058e+02 0.435 0.6635
## tests_taken.l4 1.065e-01 5.116e-02 2.081 0.0381 *
## case_count.l4 -6.649e-01 6.238e-01 -1.066 0.2871
## vaccine_doses_administered.l4 3.390e-02 9.956e-02 0.340 0.7337
## mobility_mean.l4 1.018e+02 6.064e+02 0.168 0.8668
## tests_taken.l5 7.150e-02 5.076e-02 1.409 0.1598
## case_count.l5 2.469e+00 6.218e-01 3.970 8.64e-05 ***
## vaccine_doses_administered.l5 3.676e-02 9.988e-02 0.368 0.7131
## mobility_mean.l5 3.655e+01 6.044e+02 0.060 0.9518
## tests_taken.l6 1.121e-01 5.061e-02 2.214 0.0274 *
## case_count.l6 1.062e-01 6.305e-01 0.168 0.8663
## vaccine_doses_administered.l6 -1.647e-01 1.005e-01 -1.639 0.1020
## mobility_mean.l6 -2.214e+02 6.021e+02 -0.368 0.7133
## tests_taken.l7 9.479e-02 5.045e-02 1.879 0.0611 .
## case_count.l7 -2.385e-01 6.326e-01 -0.377 0.7064
## vaccine_doses_administered.l7 8.254e-02 1.019e-01 0.810 0.4183
## mobility_mean.l7 -1.385e+01 6.003e+02 -0.023 0.9816
## tests_taken.l8 -3.639e-03 4.978e-02 -0.073 0.9418
## case_count.l8 2.585e-01 6.070e-01 0.426 0.6705
## vaccine_doses_administered.l8 -7.832e-03 8.261e-02 -0.095 0.9245
## mobility_mean.l8 -4.741e+01 5.164e+02 -0.092 0.9269
## const 4.185e+04 8.026e+03 5.214 3.08e-07 ***
## sd1 8.388e+02 1.114e+04 0.075 0.9400
## sd2 -7.518e+03 1.259e+04 -0.597 0.5509
## sd3 3.743e+01 1.078e+04 0.003 0.9972
## sd4 4.356e+03 1.073e+04 0.406 0.6850
## sd5 9.403e+03 1.256e+04 0.749 0.4545
## sd6 -7.825e+03 1.140e+04 -0.686 0.4931
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 34010 on 369 degrees of freedom
## Multiple R-Squared: 0.512, Adjusted R-squared: 0.4618
## F-statistic: 10.19 on 38 and 369 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count:
## ===========================================
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.235e-03 4.390e-03 0.281 0.778661
## case_count.l1 3.400e-01 5.146e-02 6.607 1.37e-10 ***
## vaccine_doses_administered.l1 1.524e-02 6.842e-03 2.228 0.026506 *
## mobility_mean.l1 2.130e+02 4.172e+01 5.107 5.27e-07 ***
## tests_taken.l2 8.413e-03 4.363e-03 1.928 0.054585 .
## case_count.l2 -5.779e-02 5.319e-02 -1.087 0.277928
## vaccine_doses_administered.l2 -7.426e-03 8.505e-03 -0.873 0.383109
## mobility_mean.l2 -9.565e+01 5.083e+01 -1.882 0.060643 .
## tests_taken.l3 1.230e-02 4.341e-03 2.833 0.004861 **
## case_count.l3 9.092e-02 5.216e-02 1.743 0.082145 .
## vaccine_doses_administered.l3 1.184e-02 8.434e-03 1.404 0.161255
## mobility_mean.l3 -4.930e+01 5.107e+01 -0.965 0.334961
## tests_taken.l4 7.756e-04 4.313e-03 0.180 0.857385
## case_count.l4 1.178e-01 5.258e-02 2.240 0.025653 *
## vaccine_doses_administered.l4 -1.221e-02 8.392e-03 -1.455 0.146419
## mobility_mean.l4 -9.871e+01 5.112e+01 -1.931 0.054273 .
## tests_taken.l5 -3.491e-03 4.279e-03 -0.816 0.415055
## case_count.l5 -3.462e-02 5.242e-02 -0.660 0.509360
## vaccine_doses_administered.l5 5.389e-03 8.419e-03 0.640 0.522507
## mobility_mean.l5 2.474e+01 5.095e+01 0.486 0.627510
## tests_taken.l6 -6.714e-03 4.267e-03 -1.574 0.116406
## case_count.l6 2.537e-01 5.315e-02 4.773 2.62e-06 ***
## vaccine_doses_administered.l6 2.364e-03 8.469e-03 0.279 0.780314
## mobility_mean.l6 -1.929e+01 5.075e+01 -0.380 0.704100
## tests_taken.l7 -9.989e-03 4.253e-03 -2.349 0.019372 *
## case_count.l7 1.961e-01 5.333e-02 3.677 0.000271 ***
## vaccine_doses_administered.l7 -1.630e-02 8.587e-03 -1.898 0.058429 .
## mobility_mean.l7 -2.859e+01 5.061e+01 -0.565 0.572412
## tests_taken.l8 -3.717e-03 4.196e-03 -0.886 0.376326
## case_count.l8 4.592e-02 5.117e-02 0.897 0.370140
## vaccine_doses_administered.l8 -3.096e-03 6.964e-03 -0.445 0.656931
## mobility_mean.l8 7.231e+01 4.353e+01 1.661 0.097495 .
## const 9.233e+02 6.765e+02 1.365 0.173142
## sd1 2.530e+03 9.391e+02 2.695 0.007369 **
## sd2 6.526e+03 1.062e+03 6.148 2.04e-09 ***
## sd3 5.293e+03 9.088e+02 5.824 1.25e-08 ***
## sd4 3.452e+03 9.043e+02 3.817 0.000158 ***
## sd5 3.993e+03 1.059e+03 3.772 0.000189 ***
## sd6 4.626e+03 9.613e+02 4.813 2.18e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2867 on 369 degrees of freedom
## Multiple R-Squared: 0.8018, Adjusted R-squared: 0.7814
## F-statistic: 39.28 on 38 and 369 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -1.859e-02 2.986e-02 -0.622 0.53409
## case_count.l1 -5.233e-01 3.501e-01 -1.494 0.13593
## vaccine_doses_administered.l1 8.641e-01 4.655e-02 18.564 < 2e-16 ***
## mobility_mean.l1 1.360e+02 2.838e+02 0.479 0.63214
## tests_taken.l2 1.568e-02 2.968e-02 0.528 0.59773
## case_count.l2 1.304e-01 3.619e-01 0.360 0.71871
## vaccine_doses_administered.l2 -1.053e-01 5.786e-02 -1.819 0.06974 .
## mobility_mean.l2 6.902e+02 3.458e+02 1.996 0.04669 *
## tests_taken.l3 1.537e-03 2.953e-02 0.052 0.95852
## case_count.l3 -5.666e-02 3.549e-01 -0.160 0.87323
## vaccine_doses_administered.l3 -6.816e-02 5.739e-02 -1.188 0.23570
## mobility_mean.l3 -1.644e+01 3.474e+02 -0.047 0.96228
## tests_taken.l4 -2.290e-02 2.934e-02 -0.780 0.43568
## case_count.l4 6.357e-02 3.578e-01 0.178 0.85907
## vaccine_doses_administered.l4 1.358e-01 5.710e-02 2.377 0.01794 *
## mobility_mean.l4 -4.604e+00 3.478e+02 -0.013 0.98945
## tests_taken.l5 1.641e-02 2.911e-02 0.564 0.57344
## case_count.l5 2.202e-01 3.566e-01 0.617 0.53740
## vaccine_doses_administered.l5 -1.290e-01 5.729e-02 -2.253 0.02487 *
## mobility_mean.l5 -3.442e+02 3.466e+02 -0.993 0.32141
## tests_taken.l6 -1.055e-02 2.903e-02 -0.363 0.71659
## case_count.l6 -6.214e-01 3.616e-01 -1.718 0.08656 .
## vaccine_doses_administered.l6 1.894e-01 5.762e-02 3.288 0.00111 **
## mobility_mean.l6 -3.471e+02 3.453e+02 -1.005 0.31542
## tests_taken.l7 2.781e-02 2.894e-02 0.961 0.33714
## case_count.l7 5.334e-01 3.628e-01 1.470 0.14237
## vaccine_doses_administered.l7 5.655e-01 5.842e-02 9.680 < 2e-16 ***
## mobility_mean.l7 -2.596e+02 3.443e+02 -0.754 0.45128
## tests_taken.l8 -8.422e-03 2.855e-02 -0.295 0.76817
## case_count.l8 1.124e-01 3.482e-01 0.323 0.74698
## vaccine_doses_administered.l8 -4.795e-01 4.738e-02 -10.118 < 2e-16 ***
## mobility_mean.l8 -1.992e+02 2.962e+02 -0.673 0.50156
## const -1.523e+02 4.603e+03 -0.033 0.97363
## sd1 2.679e+04 6.389e+03 4.193 3.45e-05 ***
## sd2 8.533e+03 7.223e+03 1.181 0.23821
## sd3 1.639e+04 6.184e+03 2.650 0.00839 **
## sd4 1.796e+04 6.153e+03 2.919 0.00373 **
## sd5 1.698e+04 7.202e+03 2.357 0.01894 *
## sd6 5.478e+03 6.541e+03 0.838 0.40283
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 19510 on 369 degrees of freedom
## Multiple R-Squared: 0.9446, Adjusted R-squared: 0.9389
## F-statistic: 165.4 on 38 and 369 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + tests_taken.l8 + case_count.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.937e-06 5.577e-06 0.347 0.728609
## case_count.l1 -1.307e-04 6.539e-05 -1.998 0.046398 *
## vaccine_doses_administered.l1 7.439e-06 8.693e-06 0.856 0.392660
## mobility_mean.l1 6.660e-01 5.300e-02 12.565 < 2e-16 ***
## tests_taken.l2 -2.298e-06 5.543e-06 -0.414 0.678783
## case_count.l2 -2.749e-05 6.758e-05 -0.407 0.684422
## vaccine_doses_administered.l2 -1.243e-05 1.081e-05 -1.150 0.250898
## mobility_mean.l2 1.060e-01 6.458e-02 1.642 0.101521
## tests_taken.l3 5.824e-06 5.515e-06 1.056 0.291639
## case_count.l3 -1.003e-04 6.627e-05 -1.513 0.131078
## vaccine_doses_administered.l3 8.217e-06 1.072e-05 0.767 0.443702
## mobility_mean.l3 -1.331e-02 6.488e-02 -0.205 0.837616
## tests_taken.l4 -1.148e-05 5.480e-06 -2.095 0.036813 *
## case_count.l4 2.033e-05 6.681e-05 0.304 0.761104
## vaccine_doses_administered.l4 -8.784e-06 1.066e-05 -0.824 0.410585
## mobility_mean.l4 6.763e-02 6.495e-02 1.041 0.298480
## tests_taken.l5 -3.308e-06 5.437e-06 -0.608 0.543230
## case_count.l5 3.920e-05 6.660e-05 0.589 0.556519
## vaccine_doses_administered.l5 8.460e-07 1.070e-05 0.079 0.937008
## mobility_mean.l5 -5.149e-02 6.473e-02 -0.795 0.426901
## tests_taken.l6 1.917e-06 5.421e-06 0.354 0.723866
## case_count.l6 -1.843e-05 6.753e-05 -0.273 0.785096
## vaccine_doses_administered.l6 7.248e-06 1.076e-05 0.674 0.501008
## mobility_mean.l6 7.490e-02 6.448e-02 1.162 0.246183
## tests_taken.l7 1.013e-06 5.404e-06 0.188 0.851352
## case_count.l7 3.703e-05 6.776e-05 0.546 0.585069
## vaccine_doses_administered.l7 -9.222e-06 1.091e-05 -0.845 0.398499
## mobility_mean.l7 1.058e-01 6.430e-02 1.646 0.100656
## tests_taken.l8 2.992e-06 5.332e-06 0.561 0.574975
## case_count.l8 1.035e-04 6.502e-05 1.592 0.112188
## vaccine_doses_administered.l8 6.353e-06 8.849e-06 0.718 0.473253
## mobility_mean.l8 -7.723e-02 5.530e-02 -1.396 0.163424
## const -2.965e-01 8.596e-01 -0.345 0.730365
## sd1 -2.067e+00 1.193e+00 -1.733 0.083994 .
## sd2 1.366e+00 1.349e+00 1.013 0.311946
## sd3 1.504e+00 1.155e+00 1.303 0.193508
## sd4 9.989e-01 1.149e+00 0.869 0.385198
## sd5 -1.038e+00 1.345e+00 -0.772 0.440728
## sd6 4.286e+00 1.221e+00 3.509 0.000505 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.642 on 369 degrees of freedom
## Multiple R-Squared: 0.7629, Adjusted R-squared: 0.7384
## F-statistic: 31.24 on 38 and 369 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1.157e+09 2708450.0 19760118
## case_count 2.708e+06 8218347.5 2961014
## vaccine_doses_administered 1.976e+07 2961013.7 380451997
## mobility_mean 9.343e+02 406.1 18685
## mobility_mean
## tests_taken 934.32
## case_count 406.13
## vaccine_doses_administered 18684.52
## mobility_mean 13.27
##
## Correlation matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1.000000 0.02778 0.02979
## case_count 0.027781 1.00000 0.05295
## vaccine_doses_administered 0.029789 0.05295 1.00000
## mobility_mean 0.007543 0.03889 0.26299
## mobility_mean
## tests_taken 0.007543
## case_count 0.038894
## vaccine_doses_administered 0.262991
## mobility_mean 1.000000
preds=predict(fit2a,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced)[1],1),covid_reduced$case_count, type = "l")
lines(seq((dim(covid_reduced)[1]-20),dim(covid_reduced)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced$case_count,21), type = "l",ylim=c(400,5900))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit2a = mean((tail(covid_reduced$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2)
short_ASE_fit2a
## [1] 4269497
short_ASE_fit2a^.5
## [1] 2066.276
#7 Day RMSE of 2066.2 which is much lower than the 2981 from our ARIMA(6,1,14) model but higher than fit 1a
#Maybe try to look up rolling window version
long_ASE_fit2a = mean((tail(covid_reduced$case_count,21)-preds$fcst$case_count[,1])^2)
long_ASE_fit2a
## [1] 2316924
long_ASE_fit2a^.5
## [1] 1522.145
#21 Day RMSE of 1522.145 which is much lower than the 3806 from our ARIMA(6,1,14) model but higher than fit 1a
#Maybe try to look up rolling window version
#Fit based on BIC
fit2b=VAR(covid_reduced,p=2,type="const",season = 7)
summary(fit2b)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean
## Deterministic variables: const
## Sample size: 414
## Log Likelihood: -14786.812
## Roots of the characteristic polynomial:
## 0.9374 0.8802 0.7942 0.4141 0.4141 0.3528 0.1909 0.1645
## Call:
## VAR(y = covid_reduced, p = 2, type = "const", season = 7L)
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.061e-01 4.883e-02 2.174 0.0303 *
## case_count.l1 2.270e+00 5.045e-01 4.500 8.93e-06 ***
## vaccine_doses_administered.l1 6.495e-02 6.348e-02 1.023 0.3068
## mobility_mean.l1 4.125e+02 4.950e+02 0.833 0.4051
## tests_taken.l2 8.290e-02 4.689e-02 1.768 0.0778 .
## case_count.l2 2.291e+00 5.410e-01 4.235 2.84e-05 ***
## vaccine_doses_administered.l2 -2.308e-03 6.375e-02 -0.036 0.9711
## mobility_mean.l2 -8.240e+01 4.859e+02 -0.170 0.8654
## const 4.459e+04 5.699e+03 7.825 4.59e-14 ***
## sd1 1.255e+04 7.643e+03 1.642 0.1013
## sd2 6.541e+03 9.897e+03 0.661 0.5091
## sd3 -4.083e+03 7.999e+03 -0.511 0.6100
## sd4 -1.095e+03 7.556e+03 -0.145 0.8848
## sd5 7.534e+03 7.554e+03 0.997 0.3192
## sd6 -7.319e+03 8.238e+03 -0.888 0.3748
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 35850 on 399 degrees of freedom
## Multiple R-Squared: 0.4222, Adjusted R-squared: 0.402
## F-statistic: 20.83 on 14 and 399 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count:
## ===========================================
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.261e-02 4.546e-03 2.774 0.00579 **
## case_count.l1 6.176e-01 4.697e-02 13.148 < 2e-16 ***
## vaccine_doses_administered.l1 2.862e-03 5.910e-03 0.484 0.62847
## mobility_mean.l1 1.975e+02 4.608e+01 4.285 2.29e-05 ***
## tests_taken.l2 1.950e-02 4.366e-03 4.467 1.03e-05 ***
## case_count.l2 2.948e-02 5.037e-02 0.585 0.55864
## vaccine_doses_administered.l2 -7.114e-03 5.935e-03 -1.199 0.23138
## mobility_mean.l2 -2.479e+02 4.524e+01 -5.480 7.55e-08 ***
## const -8.120e+02 5.305e+02 -1.530 0.12670
## sd1 4.596e+03 7.115e+02 6.459 3.06e-10 ***
## sd2 8.193e+03 9.214e+02 8.892 < 2e-16 ***
## sd3 4.452e+03 7.447e+02 5.978 5.02e-09 ***
## sd4 3.384e+03 7.034e+02 4.810 2.14e-06 ***
## sd5 4.302e+03 7.033e+02 6.117 2.28e-09 ***
## sd6 4.700e+03 7.669e+02 6.128 2.14e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3337 on 399 degrees of freedom
## Multiple R-Squared: 0.7107, Adjusted R-squared: 0.7005
## F-statistic: 70 on 14 and 399 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -6.314e-02 3.816e-02 -1.654 0.0988 .
## case_count.l1 -2.940e-01 3.943e-01 -0.746 0.4564
## vaccine_doses_administered.l1 1.108e+00 4.961e-02 22.340 < 2e-16 ***
## mobility_mean.l1 -2.160e+02 3.869e+02 -0.558 0.5769
## tests_taken.l2 7.185e-02 3.665e-02 1.961 0.0506 .
## case_count.l2 1.204e-01 4.228e-01 0.285 0.7760
## vaccine_doses_administered.l2 -2.002e-01 4.982e-02 -4.017 7.03e-05 ***
## mobility_mean.l2 2.564e+02 3.798e+02 0.675 0.5000
## const 8.364e+03 4.454e+03 1.878 0.0611 .
## sd1 7.548e+04 5.973e+03 12.637 < 2e-16 ***
## sd2 3.465e+04 7.735e+03 4.480 9.78e-06 ***
## sd3 3.712e+04 6.252e+03 5.937 6.31e-09 ***
## sd4 3.332e+04 5.905e+03 5.642 3.19e-08 ***
## sd5 3.658e+04 5.904e+03 6.196 1.45e-09 ***
## sd6 -7.904e+03 6.438e+03 -1.228 0.2203
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 28020 on 399 degrees of freedom
## Multiple R-Squared: 0.8783, Adjusted R-squared: 0.874
## F-statistic: 205.6 on 14 and 399 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 4.762e-06 4.978e-06 0.957 0.339344
## case_count.l1 -1.095e-04 5.144e-05 -2.129 0.033852 *
## vaccine_doses_administered.l1 3.571e-06 6.472e-06 0.552 0.581379
## mobility_mean.l1 6.905e-01 5.046e-02 13.682 < 2e-16 ***
## tests_taken.l2 1.959e-06 4.781e-06 0.410 0.682227
## case_count.l2 -7.118e-05 5.515e-05 -1.291 0.197606
## vaccine_doses_administered.l2 -4.228e-06 6.499e-06 -0.651 0.515734
## mobility_mean.l2 1.282e-01 4.954e-02 2.589 0.009980 **
## const -1.152e+00 5.810e-01 -1.983 0.048066 *
## sd1 -2.951e+00 7.792e-01 -3.787 0.000176 ***
## sd2 1.134e+00 1.009e+00 1.124 0.261740
## sd3 2.597e+00 8.155e-01 3.184 0.001564 **
## sd4 2.020e+00 7.703e-01 2.623 0.009059 **
## sd5 -1.612e+00 7.702e-01 -2.093 0.037008 *
## sd6 4.883e+00 8.399e-01 5.814 1.25e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.655 on 399 degrees of freedom
## Multiple R-Squared: 0.7435, Adjusted R-squared: 0.7345
## F-statistic: 82.6 on 14 and 399 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1284949096 7335889.6 -25228520
## case_count 7335890 11137605.8 -7740908
## vaccine_doses_administered -25228520 -7740908.5 784939569
## mobility_mean 1592 291.8 17647
## mobility_mean
## tests_taken 1591.92
## case_count 291.84
## vaccine_doses_administered 17647.35
## mobility_mean 13.36
##
## Correlation matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1.00000 0.06132 -0.02512
## case_count 0.06132 1.00000 -0.08279
## vaccine_doses_administered -0.02512 -0.08279 1.00000
## mobility_mean 0.01215 0.02393 0.17235
## mobility_mean
## tests_taken 0.01215
## case_count 0.02393
## vaccine_doses_administered 0.17235
## mobility_mean 1.00000
preds=predict(fit2b,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced)[1],1),covid_reduced$case_count, type = "l")
lines(seq((dim(covid_reduced)[1]-20),dim(covid_reduced)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced$case_count,21), type = "l",ylim=c(400,5900))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit2b = mean((tail(covid_reduced$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2)
short_ASE_fit2b
## [1] 2546313
short_ASE_fit2b^.5
## [1] 1595.717
#7 Day RMSE of 1595.7 which is much lower than the 2981 from our ARIMA(6,1,14) model and higher than fit 1a
#Maybe try to look up rolling window version
long_ASE_fit2b = mean((tail(covid_reduced$case_count,21)-preds$fcst$case_count[,1])^2)
long_ASE_fit2b
## [1] 6947698
long_ASE_fit2b^.5
## [1] 2635.849
#21 Day RMSE of 2635.8 which is much lower than the 3806 from our ARIMA(6,1,14) model but higher than fit 1a
#Maybe try to look up rolling window version
#Test a first differenced data set
VARselect(covid_d1,lag.max = 25,type = 'const')
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 7 7 7 7
##
## $criteria
## 1 2 3 4 5
## AIC(n) 6.218100e+01 6.174680e+01 6.143869e+01 6.130257e+01 6.049874e+01
## HQ(n) 6.226163e+01 6.189193e+01 6.164832e+01 6.157670e+01 6.083737e+01
## SC(n) 6.238440e+01 6.211291e+01 6.196751e+01 6.199411e+01 6.135299e+01
## FPE(n) 1.011275e+27 6.551032e+26 4.814222e+26 4.202097e+26 1.881270e+26
## 6 7 8 9 10
## AIC(n) 6.014111e+01 5.975010e+01 5.975529e+01 5.975026e+01 5.976555e+01
## HQ(n) 6.054424e+01 6.021773e+01 6.028742e+01 6.034689e+01 6.042668e+01
## SC(n) 6.115807e+01 6.092977e+01 6.109768e+01 6.125536e+01 6.143337e+01
## FPE(n) 1.316004e+26 8.904607e+25 8.955637e+25 8.916648e+25 9.061565e+25
## 11 12 13 14 15
## AIC(n) 5.979913e+01 5.981682e+01 5.982840e+01 5.978511e+01 5.981326e+01
## HQ(n) 6.052476e+01 6.060696e+01 6.068303e+01 6.070425e+01 6.079690e+01
## SC(n) 6.162965e+01 6.181007e+01 6.198436e+01 6.210378e+01 6.229465e+01
## FPE(n) 9.380451e+25 9.559516e+25 9.684646e+25 9.289814e+25 9.573416e+25
## 16 17 18 19 20
## AIC(n) 5.980962e+01 5.983894e+01 5.987629e+01 5.988328e+01 5.991005e+01
## HQ(n) 6.085775e+01 6.095158e+01 6.105343e+01 6.112492e+01 6.121618e+01
## SC(n) 6.245371e+01 6.264576e+01 6.284582e+01 6.301552e+01 6.320500e+01
## FPE(n) 9.559579e+25 9.868698e+25 1.027312e+26 1.037782e+26 1.069684e+26
## 21 22 23 24 25
## AIC(n) 5.984962e+01 5.986197e+01 5.991650e+01 5.997629e+01 5.998206e+01
## HQ(n) 6.122026e+01 6.129711e+01 6.141614e+01 6.154043e+01 6.161070e+01
## SC(n) 6.330729e+01 6.348235e+01 6.369959e+01 6.392210e+01 6.409059e+01
## FPE(n) 1.010889e+26 1.027858e+26 1.090607e+26 1.163809e+26 1.177185e+26
#AIC 7, BIC 7
#Fit based on AIC
fit3a=VAR(covid_d1,p=7,type="const")
summary(fit3a)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean
## Deterministic variables: const
## Sample size: 408
## Log Likelihood: -14376.36
## Roots of the characteristic polynomial:
## 0.9871 0.9871 0.9839 0.9839 0.9472 0.9472 0.9275 0.9275 0.905 0.905 0.8003 0.8003 0.7986 0.7986 0.7956 0.7956 0.7355 0.7355 0.7053 0.7053 0.6303 0.6303 0.5913 0.5794 0.5794 0.5001 0.2447 0.133
## Call:
## VAR(y = covid_d1, p = 7, type = "const")
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -0.90447 0.05129 -17.634 < 2e-16 ***
## case_count.l1 1.48701 0.59758 2.488 0.01326 *
## vaccine_doses_administered.l1 0.06037 0.07560 0.799 0.42504
## mobility_mean.l1 423.80902 467.77508 0.906 0.36551
## tests_taken.l2 -0.83550 0.06781 -12.320 < 2e-16 ***
## case_count.l2 1.90671 0.67209 2.837 0.00480 **
## vaccine_doses_administered.l2 0.04006 0.07768 0.516 0.60634
## mobility_mean.l2 541.58287 491.15846 1.103 0.27087
## tests_taken.l3 -0.81429 0.07644 -10.653 < 2e-16 ***
## case_count.l3 2.29467 0.70474 3.256 0.00123 **
## vaccine_doses_administered.l3 0.08583 0.07563 1.135 0.25714
## mobility_mean.l3 565.58403 503.73724 1.123 0.26224
## tests_taken.l4 -0.60045 0.08260 -7.269 2.09e-12 ***
## case_count.l4 0.61988 0.72958 0.850 0.39606
## vaccine_doses_administered.l4 0.12798 0.07851 1.630 0.10390
## mobility_mean.l4 603.77284 511.44652 1.181 0.23853
## tests_taken.l5 -0.42061 0.07733 -5.439 9.63e-08 ***
## case_count.l5 2.27264 0.68974 3.295 0.00108 **
## vaccine_doses_administered.l5 0.09277 0.07654 1.212 0.22627
## mobility_mean.l5 718.53244 512.61627 1.402 0.16182
## tests_taken.l6 -0.21499 0.06715 -3.202 0.00148 **
## case_count.l6 1.64501 0.67278 2.445 0.01494 *
## vaccine_doses_administered.l6 -0.03959 0.07755 -0.511 0.60996
## mobility_mean.l6 494.73207 506.21445 0.977 0.32904
## tests_taken.l7 -0.04047 0.04994 -0.810 0.41826
## case_count.l7 0.61948 0.59887 1.034 0.30160
## vaccine_doses_administered.l7 0.07038 0.07721 0.911 0.36262
## mobility_mean.l7 22.31164 477.72695 0.047 0.96277
## const 46.04632 1754.01731 0.026 0.97907
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 35400 on 379 degrees of freedom
## Multiple R-Squared: 0.5179, Adjusted R-squared: 0.4822
## F-statistic: 14.54 on 28 and 379 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count:
## ===========================================
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.940e-03 4.404e-03 0.440 0.65987
## case_count.l1 -6.199e-01 5.130e-02 -12.082 < 2e-16 ***
## vaccine_doses_administered.l1 2.867e-02 6.490e-03 4.418 1.30e-05 ***
## mobility_mean.l1 1.233e+02 4.016e+01 3.071 0.00229 **
## tests_taken.l2 9.386e-03 5.822e-03 1.612 0.10778
## case_count.l2 -7.281e-01 5.770e-02 -12.618 < 2e-16 ***
## vaccine_doses_administered.l2 3.664e-03 6.669e-03 0.549 0.58304
## mobility_mean.l2 7.881e+01 4.217e+01 1.869 0.06242 .
## tests_taken.l3 1.910e-02 6.563e-03 2.911 0.00381 **
## case_count.l3 -6.465e-01 6.051e-02 -10.685 < 2e-16 ***
## vaccine_doses_administered.l3 1.282e-02 6.493e-03 1.974 0.04912 *
## mobility_mean.l3 7.598e+01 4.325e+01 1.757 0.07974 .
## tests_taken.l4 1.922e-02 7.092e-03 2.710 0.00704 **
## case_count.l4 -5.534e-01 6.264e-02 -8.835 < 2e-16 ***
## vaccine_doses_administered.l4 3.782e-03 6.740e-03 0.561 0.57506
## mobility_mean.l4 -2.795e+01 4.391e+01 -0.637 0.52476
## tests_taken.l5 1.694e-02 6.639e-03 2.551 0.01113 *
## case_count.l5 -6.349e-01 5.922e-02 -10.722 < 2e-16 ***
## vaccine_doses_administered.l5 1.451e-02 6.572e-03 2.208 0.02783 *
## mobility_mean.l5 -2.274e+00 4.401e+01 -0.052 0.95882
## tests_taken.l6 1.034e-02 5.765e-03 1.794 0.07366 .
## case_count.l6 -3.504e-01 5.776e-02 -6.066 3.18e-09 ***
## vaccine_doses_administered.l6 6.431e-03 6.658e-03 0.966 0.33471
## mobility_mean.l6 6.130e+01 4.346e+01 1.410 0.15921
## tests_taken.l7 8.633e-04 4.288e-03 0.201 0.84054
## case_count.l7 -4.138e-02 5.142e-02 -0.805 0.42145
## vaccine_doses_administered.l7 3.935e-03 6.629e-03 0.594 0.55313
## mobility_mean.l7 2.841e+01 4.102e+01 0.693 0.48898
## const -4.659e+01 1.506e+02 -0.309 0.75718
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3039 on 379 degrees of freedom
## Multiple R-Squared: 0.5532, Adjusted R-squared: 0.5202
## F-statistic: 16.76 on 28 and 379 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -1.876e-02 2.918e-02 -0.643 0.520667
## case_count.l1 -6.359e-01 3.400e-01 -1.870 0.062196 .
## vaccine_doses_administered.l1 -1.589e-01 4.301e-02 -3.694 0.000253 ***
## mobility_mean.l1 1.249e+02 2.661e+02 0.469 0.639007
## tests_taken.l2 -2.066e-02 3.858e-02 -0.536 0.592562
## case_count.l2 -2.649e-01 3.824e-01 -0.693 0.488831
## vaccine_doses_administered.l2 -2.347e-01 4.420e-02 -5.310 1.87e-07 ***
## mobility_mean.l2 1.186e+03 2.795e+02 4.244 2.77e-05 ***
## tests_taken.l3 -1.964e-02 4.349e-02 -0.452 0.651868
## case_count.l3 -5.239e-01 4.010e-01 -1.307 0.192169
## vaccine_doses_administered.l3 -2.822e-01 4.303e-02 -6.558 1.79e-10 ***
## mobility_mean.l3 6.688e+02 2.866e+02 2.333 0.020150 *
## tests_taken.l4 -4.556e-02 4.700e-02 -0.969 0.333007
## case_count.l4 -6.552e-01 4.151e-01 -1.578 0.115304
## vaccine_doses_administered.l4 -1.900e-01 4.467e-02 -4.254 2.65e-05 ***
## mobility_mean.l4 1.103e+03 2.910e+02 3.792 0.000174 ***
## tests_taken.l5 -3.637e-02 4.400e-02 -0.827 0.409029
## case_count.l5 -4.807e-01 3.924e-01 -1.225 0.221393
## vaccine_doses_administered.l5 -2.849e-01 4.355e-02 -6.542 1.97e-10 ***
## mobility_mean.l5 8.364e+02 2.917e+02 2.868 0.004365 **
## tests_taken.l6 -3.694e-02 3.820e-02 -0.967 0.334274
## case_count.l6 -7.509e-01 3.828e-01 -1.962 0.050529 .
## vaccine_doses_administered.l6 -1.345e-01 4.412e-02 -3.049 0.002459 **
## mobility_mean.l6 7.774e+02 2.880e+02 2.699 0.007263 **
## tests_taken.l7 -3.253e-03 2.841e-02 -0.114 0.908915
## case_count.l7 -7.257e-02 3.407e-01 -0.213 0.831469
## vaccine_doses_administered.l7 5.672e-01 4.393e-02 12.912 < 2e-16 ***
## mobility_mean.l7 -2.799e+01 2.718e+02 -0.103 0.918044
## const 1.770e+02 9.980e+02 0.177 0.859337
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 20140 on 379 degrees of freedom
## Multiple R-Squared: 0.7616, Adjusted R-squared: 0.744
## F-statistic: 43.25 on 28 and 379 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 2.516e-06 5.515e-06 0.456 0.648465
## case_count.l1 -8.401e-05 6.425e-05 -1.307 0.191843
## vaccine_doses_administered.l1 2.158e-05 8.128e-06 2.655 0.008273 **
## mobility_mean.l1 -3.598e-01 5.030e-02 -7.154 4.39e-12 ***
## tests_taken.l2 6.155e-07 7.291e-06 0.084 0.932775
## case_count.l2 -1.397e-04 7.226e-05 -1.933 0.053941 .
## vaccine_doses_administered.l2 -6.160e-06 8.352e-06 -0.738 0.461274
## mobility_mean.l2 -2.221e-01 5.281e-02 -4.205 3.26e-05 ***
## tests_taken.l3 5.283e-06 8.219e-06 0.643 0.520747
## case_count.l3 -2.253e-04 7.577e-05 -2.974 0.003131 **
## vaccine_doses_administered.l3 6.555e-06 8.131e-06 0.806 0.420640
## mobility_mean.l3 -1.971e-01 5.416e-02 -3.640 0.000311 ***
## tests_taken.l4 -7.577e-06 8.882e-06 -0.853 0.394132
## case_count.l4 -1.679e-04 7.844e-05 -2.140 0.032978 *
## vaccine_doses_administered.l4 -1.328e-05 8.441e-06 -1.573 0.116493
## mobility_mean.l4 -9.849e-02 5.499e-02 -1.791 0.074082 .
## tests_taken.l5 -1.051e-05 8.315e-06 -1.264 0.207134
## case_count.l5 -1.356e-04 7.416e-05 -1.828 0.068347 .
## vaccine_doses_administered.l5 5.481e-06 8.230e-06 0.666 0.505847
## mobility_mean.l5 -1.996e-01 5.512e-02 -3.621 0.000334 ***
## tests_taken.l6 -6.699e-06 7.220e-06 -0.928 0.354089
## case_count.l6 -2.330e-04 7.234e-05 -3.221 0.001389 **
## vaccine_doses_administered.l6 -1.397e-06 8.338e-06 -0.168 0.866982
## mobility_mean.l6 -1.061e-01 5.443e-02 -1.949 0.052024 .
## tests_taken.l7 -6.545e-06 5.370e-06 -1.219 0.223676
## case_count.l7 -1.305e-04 6.439e-05 -2.026 0.043426 *
## vaccine_doses_administered.l7 -1.974e-05 8.302e-06 -2.377 0.017936 *
## mobility_mean.l7 1.752e-01 5.137e-02 3.411 0.000717 ***
## const 3.654e-02 1.886e-01 0.194 0.846494
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.806 on 379 degrees of freedom
## Multiple R-Squared: 0.4037, Adjusted R-squared: 0.3596
## F-statistic: 9.164 on 28 and 379 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1252895784 1918874.9 23332252
## case_count 1918875 9235203.7 4891734
## vaccine_doses_administered 23332252 4891733.7 405589362
## mobility_mean -2088 881.1 17494
## mobility_mean
## tests_taken -2088.45
## case_count 881.07
## vaccine_doses_administered 17494.43
## mobility_mean 14.48
##
## Correlation matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1.00000 0.01784 0.03273
## case_count 0.01784 1.00000 0.07993
## vaccine_doses_administered 0.03273 0.07993 1.00000
## mobility_mean -0.01550 0.07618 0.22825
## mobility_mean
## tests_taken -0.01550
## case_count 0.07618
## vaccine_doses_administered 0.22825
## mobility_mean 1.00000
preds=predict(fit3a,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_d1)[1],1),covid_d1$case_count, type = "l")
lines(seq((dim(covid_d1)[1]-20),dim(covid_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_d1$case_count,21), type = "l",ylim=c(min(preds$fcst$case_count[,2]),max(preds$fcst$case_count[,3])))
lines(preds$fcst$case_count[,1],type = "l",col='blue')
lines(preds$fcst$case_count[,2],type = "l",col='blue', lty=2)
lines(preds$fcst$case_count[,3],type = "l",col='blue', lty=2)

short_ASE_fit3a = mean((tail(covid_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2)
short_ASE_fit3a
## [1] 1635425
short_ASE_fit3a^.5
## [1] 1278.838
#7 Day RMSE of 1278.8 which is second lowest short term RMSE
#Maybe try to look up rolling window version
long_ASE_fit3a = mean((tail(covid_d1$case_count,21)-preds$fcst$case_count[,1])^2)
long_ASE_fit3a
## [1] 949245.8
long_ASE_fit3a^.5
## [1] 974.2925
#21 Day RMSE of 974.3 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest long term VAR model
#Maybe try to look up rolling window version
#Test a first differenced and seasonal data set
VARselect(covid_d1,lag.max = 25,type = 'const',season = 7)
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 7 7 7 7
##
## $criteria
## 1 2 3 4 5
## AIC(n) 6.100714e+01 6.075594e+01 6.049028e+01 6.034737e+01 5.991805e+01
## HQ(n) 6.118452e+01 6.099781e+01 6.079666e+01 6.071825e+01 6.035343e+01
## SC(n) 6.145460e+01 6.136611e+01 6.126317e+01 6.128297e+01 6.101637e+01
## FPE(n) 3.126734e+26 2.432396e+26 1.865218e+26 1.617215e+26 1.053086e+26
## 6 7 8 9 10
## AIC(n) 5.981082e+01 5.957415e+01 5.957787e+01 5.959924e+01 5.962475e+01
## HQ(n) 6.031070e+01 6.013853e+01 6.020675e+01 6.029262e+01 6.038263e+01
## SC(n) 6.107185e+01 6.099790e+01 6.116433e+01 6.134841e+01 6.153663e+01
## FPE(n) 9.464374e+25 7.474246e+25 7.507661e+25 7.676871e+25 7.883953e+25
## 11 12 13 14 15
## AIC(n) 5.965132e+01 5.967592e+01 5.972030e+01 5.968985e+01 5.971551e+01
## HQ(n) 6.047371e+01 6.056280e+01 6.067168e+01 6.070573e+01 6.079590e+01
## SC(n) 6.172592e+01 6.191323e+01 6.212033e+01 6.225259e+01 6.244097e+01
## FPE(n) 8.106958e+25 8.321674e+25 8.714897e+25 8.470920e+25 8.711545e+25
## 16 17 18 19 20
## AIC(n) 5.971280e+01 5.974522e+01 5.977376e+01 5.976680e+01 5.980942e+01
## HQ(n) 6.085768e+01 6.095461e+01 6.104765e+01 6.110519e+01 6.121230e+01
## SC(n) 6.260096e+01 6.279610e+01 6.298736e+01 6.314311e+01 6.334844e+01
## FPE(n) 8.710989e+25 9.024940e+25 9.317183e+25 9.286860e+25 9.730909e+25
## 21 22 23 24 25
## AIC(n) 5.976474e+01 5.978821e+01 5.983441e+01 5.988911e+01 5.989082e+01
## HQ(n) 6.123213e+01 6.132010e+01 6.143080e+01 6.155000e+01 6.161621e+01
## SC(n) 6.346648e+01 6.365266e+01 6.386157e+01 6.407899e+01 6.424341e+01
## FPE(n) 9.347804e+25 9.617226e+25 1.012660e+26 1.075929e+26 1.084703e+26
#AIC 7, BIC 7
#Fit based on AIC
fit4a=VAR(covid_d1,p=7,type="const",season = 7)
summary(fit4a)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, case_count, vaccine_doses_administered, mobility_mean
## Deterministic variables: const
## Sample size: 408
## Log Likelihood: -14314.892
## Roots of the characteristic polynomial:
## 0.9733 0.9733 0.9478 0.9478 0.8905 0.8905 0.89 0.89 0.8379 0.8379 0.788 0.788 0.7609 0.7609 0.7495 0.7495 0.7251 0.7251 0.6716 0.6716 0.6438 0.6438 0.5927 0.5927 0.5879 0.5879 0.4473 0.4473
## Call:
## VAR(y = covid_d1, p = 7, type = "const", season = 7L)
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -9.024e-01 5.164e-02 -17.475 < 2e-16 ***
## case_count.l1 1.343e+00 6.307e-01 2.129 0.03393 *
## vaccine_doses_administered.l1 8.995e-02 8.404e-02 1.070 0.28517
## mobility_mean.l1 1.645e+02 5.081e+02 0.324 0.74636
## tests_taken.l2 -8.318e-01 6.833e-02 -12.174 < 2e-16 ***
## case_count.l2 1.535e+00 7.249e-01 2.117 0.03491 *
## vaccine_doses_administered.l2 -6.741e-04 8.537e-02 -0.008 0.99370
## mobility_mean.l2 6.161e+02 5.440e+02 1.133 0.25808
## tests_taken.l3 -8.106e-01 7.715e-02 -10.507 < 2e-16 ***
## case_count.l3 2.008e+00 7.693e-01 2.610 0.00942 **
## vaccine_doses_administered.l3 7.935e-02 8.360e-02 0.949 0.34310
## mobility_mean.l3 8.026e+02 5.564e+02 1.443 0.14999
## tests_taken.l4 -5.907e-01 8.359e-02 -7.066 7.89e-12 ***
## case_count.l4 5.752e-01 7.936e-01 0.725 0.46904
## vaccine_doses_administered.l4 1.138e-01 8.717e-02 1.306 0.19242
## mobility_mean.l4 7.874e+02 5.691e+02 1.384 0.16732
## tests_taken.l5 -4.080e-01 7.841e-02 -5.204 3.23e-07 ***
## case_count.l5 2.374e+00 7.512e-01 3.160 0.00170 **
## vaccine_doses_administered.l5 1.353e-01 8.385e-02 1.614 0.10742
## mobility_mean.l5 6.513e+02 5.708e+02 1.141 0.25464
## tests_taken.l6 -2.025e-01 6.837e-02 -2.962 0.00326 **
## case_count.l6 1.625e+00 7.100e-01 2.289 0.02264 *
## vaccine_doses_administered.l6 -4.232e-02 8.522e-02 -0.497 0.61979
## mobility_mean.l6 3.422e+02 5.644e+02 0.606 0.54470
## tests_taken.l7 -3.874e-02 5.101e-02 -0.759 0.44813
## case_count.l7 7.410e-01 6.088e-01 1.217 0.22435
## vaccine_doses_administered.l7 4.837e-02 8.511e-02 0.568 0.57013
## mobility_mean.l7 2.214e+02 5.320e+02 0.416 0.67747
## const 5.126e+01 1.759e+03 0.029 0.97676
## sd1 -7.788e+03 1.186e+04 -0.656 0.51198
## sd2 2.333e+03 1.324e+04 0.176 0.86024
## sd3 6.378e+03 1.133e+04 0.563 0.57373
## sd4 9.530e+03 1.130e+04 0.843 0.39956
## sd5 -8.522e+03 1.316e+04 -0.648 0.51766
## sd6 1.682e+03 1.160e+04 0.145 0.88483
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 35490 on 373 degrees of freedom
## Multiple R-Squared: 0.523, Adjusted R-squared: 0.4795
## F-statistic: 12.03 on 34 and 373 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count:
## ===========================================
## case_count = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.494e-03 4.189e-03 0.357 0.721537
## case_count.l1 -6.410e-01 5.116e-02 -12.530 < 2e-16 ***
## vaccine_doses_administered.l1 1.440e-02 6.817e-03 2.113 0.035292 *
## mobility_mean.l1 2.151e+02 4.121e+01 5.218 3.00e-07 ***
## tests_taken.l2 1.021e-02 5.542e-03 1.842 0.066210 .
## case_count.l2 -6.904e-01 5.880e-02 -11.741 < 2e-16 ***
## vaccine_doses_administered.l2 7.120e-03 6.925e-03 1.028 0.304502
## mobility_mean.l2 1.145e+02 4.412e+01 2.596 0.009808 **
## tests_taken.l3 2.266e-02 6.258e-03 3.621 0.000334 ***
## case_count.l3 -5.916e-01 6.240e-02 -9.480 < 2e-16 ***
## vaccine_doses_administered.l3 1.976e-02 6.781e-03 2.914 0.003781 **
## mobility_mean.l3 6.287e+01 4.513e+01 1.393 0.164427
## tests_taken.l4 2.337e-02 6.781e-03 3.447 0.000632 ***
## case_count.l4 -4.674e-01 6.437e-02 -7.261 2.25e-12 ***
## vaccine_doses_administered.l4 7.785e-03 7.071e-03 1.101 0.271612
## mobility_mean.l4 -3.720e+01 4.616e+01 -0.806 0.420771
## tests_taken.l5 1.990e-02 6.360e-03 3.129 0.001895 **
## case_count.l5 -4.981e-01 6.094e-02 -8.174 4.72e-15 ***
## vaccine_doses_administered.l5 1.395e-02 6.801e-03 2.051 0.040943 *
## mobility_mean.l5 -1.413e+01 4.630e+01 -0.305 0.760357
## tests_taken.l6 1.329e-02 5.546e-03 2.397 0.017023 *
## case_count.l6 -2.387e-01 5.759e-02 -4.145 4.22e-05 ***
## vaccine_doses_administered.l6 1.683e-02 6.912e-03 2.435 0.015353 *
## mobility_mean.l6 -3.520e+01 4.578e+01 -0.769 0.442485
## tests_taken.l7 3.446e-03 4.138e-03 0.833 0.405427
## case_count.l7 -4.219e-02 4.938e-02 -0.854 0.393509
## vaccine_doses_administered.l7 7.356e-04 6.903e-03 0.107 0.915192
## mobility_mean.l7 -6.666e+01 4.315e+01 -1.545 0.123235
## const -5.329e+01 1.427e+02 -0.374 0.708958
## sd1 3.982e+03 9.624e+02 4.138 4.34e-05 ***
## sd2 2.705e+03 1.074e+03 2.519 0.012189 *
## sd3 8.336e+02 9.189e+02 0.907 0.364859
## sd4 1.390e+03 9.166e+02 1.517 0.130165
## sd5 1.998e+03 1.067e+03 1.872 0.062034 .
## sd6 -2.608e+03 9.410e+02 -2.771 0.005864 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2879 on 373 degrees of freedom
## Multiple R-Squared: 0.6054, Adjusted R-squared: 0.5695
## F-statistic: 16.83 on 34 and 373 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -2.028e-02 2.855e-02 -0.710 0.47805
## case_count.l1 -4.863e-01 3.487e-01 -1.395 0.16397
## vaccine_doses_administered.l1 -1.247e-01 4.647e-02 -2.684 0.00761 **
## mobility_mean.l1 2.147e+02 2.809e+02 0.764 0.44516
## tests_taken.l2 -5.742e-03 3.778e-02 -0.152 0.87928
## case_count.l2 -3.272e-01 4.008e-01 -0.816 0.41487
## vaccine_doses_administered.l2 -2.292e-01 4.720e-02 -4.855 1.77e-06 ***
## mobility_mean.l2 9.257e+02 3.007e+02 3.078 0.00224 **
## tests_taken.l3 -6.026e-03 4.265e-02 -0.141 0.88774
## case_count.l3 -3.578e-01 4.253e-01 -0.841 0.40076
## vaccine_doses_administered.l3 -2.923e-01 4.622e-02 -6.323 7.33e-10 ***
## mobility_mean.l3 9.314e+02 3.076e+02 3.028 0.00263 **
## tests_taken.l4 -3.138e-02 4.622e-02 -0.679 0.49754
## case_count.l4 -2.523e-01 4.388e-01 -0.575 0.56561
## vaccine_doses_administered.l4 -1.542e-01 4.820e-02 -3.198 0.00150 **
## mobility_mean.l4 9.498e+02 3.146e+02 3.019 0.00271 **
## tests_taken.l5 -1.505e-02 4.335e-02 -0.347 0.72873
## case_count.l5 -1.993e-02 4.154e-01 -0.048 0.96175
## vaccine_doses_administered.l5 -2.795e-01 4.636e-02 -6.030 3.96e-09 ***
## mobility_mean.l5 6.219e+02 3.156e+02 1.971 0.04951 *
## tests_taken.l6 -2.482e-02 3.780e-02 -0.657 0.51185
## case_count.l6 -6.294e-01 3.926e-01 -1.603 0.10968
## vaccine_doses_administered.l6 -8.583e-02 4.712e-02 -1.822 0.06929 .
## mobility_mean.l6 3.081e+02 3.120e+02 0.987 0.32408
## tests_taken.l7 4.936e-03 2.820e-02 0.175 0.86117
## case_count.l7 -1.116e-01 3.366e-01 -0.332 0.74033
## vaccine_doses_administered.l7 4.797e-01 4.705e-02 10.195 < 2e-16 ***
## mobility_mean.l7 8.756e+01 2.941e+02 0.298 0.76610
## const 1.835e+02 9.724e+02 0.189 0.85046
## sd1 -1.783e+04 6.560e+03 -2.717 0.00689 **
## sd2 -1.041e+04 7.321e+03 -1.422 0.15577
## sd3 -9.238e+03 6.263e+03 -1.475 0.14106
## sd4 -1.032e+04 6.248e+03 -1.651 0.09956 .
## sd5 -2.163e+04 7.276e+03 -2.973 0.00314 **
## sd6 -2.768e+04 6.414e+03 -4.316 2.04e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 19620 on 373 degrees of freedom
## Multiple R-Squared: 0.7773, Adjusted R-squared: 0.757
## F-statistic: 38.29 on 34 and 373 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + case_count.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + tests_taken.l2 + case_count.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + tests_taken.l3 + case_count.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + tests_taken.l4 + case_count.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + tests_taken.l5 + case_count.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + tests_taken.l6 + case_count.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + tests_taken.l7 + case_count.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.296e-06 5.363e-06 0.242 0.80918
## case_count.l1 -1.269e-04 6.549e-05 -1.938 0.05339 .
## vaccine_doses_administered.l1 8.216e-06 8.728e-06 0.941 0.34710
## mobility_mean.l1 -3.012e-01 5.277e-02 -5.708 2.33e-08 ***
## tests_taken.l2 -1.486e-06 7.096e-06 -0.209 0.83428
## case_count.l2 -1.473e-04 7.528e-05 -1.956 0.05117 .
## vaccine_doses_administered.l2 -4.498e-06 8.865e-06 -0.507 0.61223
## mobility_mean.l2 -1.829e-01 5.649e-02 -3.239 0.00131 **
## tests_taken.l3 3.995e-06 8.012e-06 0.499 0.61832
## case_count.l3 -2.374e-04 7.989e-05 -2.972 0.00315 **
## vaccine_doses_administered.l3 3.982e-06 8.681e-06 0.459 0.64672
## mobility_mean.l3 -1.846e-01 5.778e-02 -3.194 0.00152 **
## tests_taken.l4 -7.695e-06 8.681e-06 -0.886 0.37594
## case_count.l4 -2.020e-04 8.241e-05 -2.451 0.01470 *
## vaccine_doses_administered.l4 -5.125e-06 9.053e-06 -0.566 0.57164
## mobility_mean.l4 -1.058e-01 5.910e-02 -1.791 0.07416 .
## tests_taken.l5 -1.032e-05 8.143e-06 -1.267 0.20594
## case_count.l5 -1.527e-04 7.802e-05 -1.957 0.05106 .
## vaccine_doses_administered.l5 -4.120e-06 8.708e-06 -0.473 0.63637
## mobility_mean.l5 -1.496e-01 5.928e-02 -2.524 0.01202 *
## tests_taken.l6 -7.414e-06 7.100e-06 -1.044 0.29709
## case_count.l6 -1.595e-04 7.373e-05 -2.164 0.03112 *
## vaccine_doses_administered.l6 3.323e-06 8.850e-06 0.376 0.70750
## mobility_mean.l6 -6.305e-02 5.861e-02 -1.076 0.28276
## tests_taken.l7 -5.002e-06 5.298e-06 -0.944 0.34564
## case_count.l7 -1.170e-04 6.323e-05 -1.851 0.06497 .
## vaccine_doses_administered.l7 -6.161e-06 8.838e-06 -0.697 0.48617
## mobility_mean.l7 5.284e-02 5.524e-02 0.956 0.33945
## const 3.120e-02 1.826e-01 0.171 0.86445
## sd1 3.584e+00 1.232e+00 2.909 0.00384 **
## sd2 3.597e+00 1.375e+00 2.616 0.00925 **
## sd3 3.023e+00 1.176e+00 2.569 0.01058 *
## sd4 9.644e-01 1.173e+00 0.822 0.41173
## sd5 6.401e+00 1.367e+00 4.683 3.96e-06 ***
## sd6 1.929e+00 1.205e+00 1.601 0.11027
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.686 on 373 degrees of freedom
## Multiple R-Squared: 0.4496, Adjusted R-squared: 0.3994
## F-statistic: 8.962 on 34 and 373 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1.260e+09 3044527.2 18250514
## case_count 3.045e+06 8287127.6 3153308
## vaccine_doses_administered 1.825e+07 3153308.2 385036896
## mobility_mean 2.713e+02 415.7 19863
## mobility_mean
## tests_taken 271.26
## case_count 415.72
## vaccine_doses_administered 19862.67
## mobility_mean 13.58
##
## Correlation matrix of residuals:
## tests_taken case_count vaccine_doses_administered
## tests_taken 1.000000 0.02980 0.02621
## case_count 0.029799 1.00000 0.05582
## vaccine_doses_administered 0.026207 0.05582 1.00000
## mobility_mean 0.002074 0.03918 0.27465
## mobility_mean
## tests_taken 0.002074
## case_count 0.039182
## vaccine_doses_administered 0.274647
## mobility_mean 1.000000
preds=predict(fit4a,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_d1)[1],1),covid_d1$case_count, type = "l")
lines(seq((dim(covid_d1)[1]-20),dim(covid_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_d1$case_count,21), type = "l",ylim=c(-3900,4600))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit4a = mean((tail(covid_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2)
short_ASE_fit4a
## [1] 1306929
short_ASE_fit4a^.5
## [1] 1143.21
#7 Day RMSE of 1143.2 which is lowest short term RMSE
#Maybe try to look up rolling window version
long_ASE_fit4a = mean((tail(covid_d1$case_count,21)-preds$fcst$case_count[,1])^2)
long_ASE_fit4a
## [1] 1405555
long_ASE_fit4a^.5
## [1] 1185.561
#21 Day RMSE of 1185.6 which is much lower than the 3806 from our ARIMA(6,1,14) model and second lowest model
#Maybe try to look up rolling window version
#Create first different response only data set
names(covid_reduced)
## [1] "tests_taken" "case_count"
## [3] "vaccine_doses_administered" "mobility_mean"
cases_d1=artrans.wge(covid_reduced$case_count,1)

covid_reduced_cases_d1=covid_reduced
covid_reduced_cases_d1$case_count_d1=c(NA,cases_d1)
names(covid_reduced_cases_d1)
## [1] "tests_taken" "case_count"
## [3] "vaccine_doses_administered" "mobility_mean"
## [5] "case_count_d1"
covid_reduced_cases_d1=covid_reduced_cases_d1[2:dim(covid_reduced_cases_d1)[1],c(1,3,4,5)]
str(covid_reduced_cases_d1)
## 'data.frame': 415 obs. of 4 variables:
## $ tests_taken : int 57352 51106 104858 124061 33404 31019 54382 79339 123081 55937 ...
## $ vaccine_doses_administered: int 0 0 0 0 0 0 0 0 0 0 ...
## $ mobility_mean : num -11.33 -11 -10.17 -11 -5.17 ...
## $ case_count_d1 : num 1372 684 -1979 -625 405 ...
#Test a first differenced cases only without seasonality
VARselect(covid_reduced_cases_d1,lag.max = 25,type = 'const')
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 8 8
##
## $criteria
## 1 2 3 4 5
## AIC(n) 6.213069e+01 6.174882e+01 6.153838e+01 6.133380e+01 6.096615e+01
## HQ(n) 6.221132e+01 6.189394e+01 6.174801e+01 6.160793e+01 6.130478e+01
## SC(n) 6.233408e+01 6.211492e+01 6.206720e+01 6.202534e+01 6.182040e+01
## FPE(n) 9.616524e+26 6.564251e+26 5.318900e+26 4.335397e+26 3.002242e+26
## 6 7 8 9 10
## AIC(n) 6.037371e+01 6.012685e+01 5.974183e+01 5.976261e+01 5.974824e+01
## HQ(n) 6.077684e+01 6.059448e+01 6.027396e+01 6.035924e+01 6.040937e+01
## SC(n) 6.139067e+01 6.130653e+01 6.108422e+01 6.126771e+01 6.141606e+01
## FPE(n) 1.660634e+26 1.297893e+26 8.835923e+25 9.027433e+25 8.906074e+25
## 11 12 13 14 15
## AIC(n) 5.975888e+01 5.978012e+01 5.980467e+01 5.980010e+01 5.977352e+01
## HQ(n) 6.048452e+01 6.057025e+01 6.065930e+01 6.071924e+01 6.075716e+01
## SC(n) 6.158941e+01 6.177337e+01 6.196063e+01 6.211877e+01 6.225490e+01
## FPE(n) 9.010459e+25 9.215016e+25 9.457529e+25 9.430139e+25 9.200426e+25
## 16 17 18 19 20
## AIC(n) 5.980352e+01 5.980417e+01 5.982964e+01 5.986458e+01 5.988051e+01
## HQ(n) 6.085165e+01 6.091680e+01 6.100678e+01 6.110622e+01 6.118665e+01
## SC(n) 6.244761e+01 6.261098e+01 6.279917e+01 6.299682e+01 6.317546e+01
## FPE(n) 9.501444e+25 9.531393e+25 9.804882e+25 1.018559e+26 1.038550e+26
## 21 22 23 24 25
## AIC(n) 5.990528e+01 5.984448e+01 5.985995e+01 5.990928e+01 5.995581e+01
## HQ(n) 6.127592e+01 6.127962e+01 6.135959e+01 6.147342e+01 6.158445e+01
## SC(n) 6.336295e+01 6.346486e+01 6.364305e+01 6.385509e+01 6.406433e+01
## FPE(n) 1.068755e+26 1.010037e+26 1.030647e+26 1.088383e+26 1.146677e+26
#AIC 8, BIC 8
#Fit based on AIC
fit5a=VAR(covid_reduced_cases_d1,p=8,type="const")
summary(fit5a)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, vaccine_doses_administered, mobility_mean, case_count_d1
## Deterministic variables: const
## Sample size: 407
## Log Likelihood: -14316.568
## Roots of the characteristic polynomial:
## 0.9871 0.9871 0.9842 0.9842 0.9839 0.9839 0.9477 0.9477 0.9347 0.9347 0.9292 0.9055 0.9055 0.8145 0.8145 0.7989 0.7989 0.7967 0.7967 0.7533 0.7533 0.7074 0.7074 0.6792 0.6792 0.657 0.657 0.6369 0.6369 0.6036 0.2768 0.1779
## Call:
## VAR(y = covid_reduced_cases_d1, p = 8, type = "const")
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 8.206e-02 5.170e-02 1.587 0.113262
## vaccine_doses_administered.l1 6.594e-02 7.651e-02 0.862 0.389345
## mobility_mean.l1 3.913e+02 4.802e+02 0.815 0.415632
## case_count_d1.l1 1.367e+00 6.065e-01 2.254 0.024805 *
## tests_taken.l2 5.245e-02 5.125e-02 1.024 0.306729
## vaccine_doses_administered.l2 -1.765e-02 8.693e-02 -0.203 0.839169
## mobility_mean.l2 1.488e+02 5.385e+02 0.276 0.782532
## case_count_d1.l2 1.867e+00 7.083e-01 2.635 0.008753 **
## tests_taken.l3 4.560e-03 5.026e-02 0.091 0.927751
## vaccine_doses_administered.l3 4.477e-02 8.699e-02 0.515 0.607075
## mobility_mean.l3 -2.184e+01 5.467e+02 -0.040 0.968164
## case_count_d1.l3 2.366e+00 8.096e-01 2.922 0.003687 **
## tests_taken.l4 2.039e-01 4.973e-02 4.099 5.08e-05 ***
## vaccine_doses_administered.l4 3.848e-02 8.641e-02 0.445 0.656304
## mobility_mean.l4 3.315e+01 5.394e+02 0.061 0.951028
## case_count_d1.l4 6.854e-01 8.224e-01 0.833 0.405098
## tests_taken.l5 1.610e-01 4.947e-02 3.255 0.001237 **
## vaccine_doses_administered.l5 -3.761e-02 8.656e-02 -0.434 0.664229
## mobility_mean.l5 1.507e+02 5.379e+02 0.280 0.779550
## case_count_d1.l5 2.369e+00 8.059e-01 2.939 0.003494 **
## tests_taken.l6 1.912e-01 4.984e-02 3.837 0.000146 ***
## vaccine_doses_administered.l6 -1.348e-01 8.719e-02 -1.546 0.122946
## mobility_mean.l6 -2.336e+02 5.376e+02 -0.434 0.664198
## case_count_d1.l6 1.762e+00 8.045e-01 2.190 0.029115 *
## tests_taken.l7 1.655e-01 5.098e-02 3.246 0.001276 **
## vaccine_doses_administered.l7 1.102e-01 8.773e-02 1.256 0.210034
## mobility_mean.l7 -4.344e+02 5.351e+02 -0.812 0.417417
## case_count_d1.l7 7.334e-01 7.069e-01 1.037 0.300189
## tests_taken.l8 3.408e-02 5.142e-02 0.663 0.507804
## vaccine_doses_administered.l8 -8.336e-02 7.776e-02 -1.072 0.284424
## mobility_mean.l8 2.913e+01 4.836e+02 0.060 0.951988
## case_count_d1.l8 3.535e-01 6.008e-01 0.588 0.556644
## const 1.197e+04 6.406e+03 1.869 0.062474 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 35410 on 374 degrees of freedom
## Multiple R-Squared: 0.4636, Adjusted R-squared: 0.4177
## F-statistic: 10.1 on 32 and 374 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -1.966e-02 2.924e-02 -0.672 0.501780
## vaccine_doses_administered.l1 8.261e-01 4.328e-02 19.089 < 2e-16 ***
## mobility_mean.l1 8.960e+01 2.716e+02 0.330 0.741673
## case_count_d1.l1 -6.734e-01 3.431e-01 -1.963 0.050397 .
## tests_taken.l2 -3.436e-03 2.899e-02 -0.119 0.905716
## vaccine_doses_administered.l2 -7.319e-02 4.917e-02 -1.489 0.137437
## mobility_mean.l2 1.028e+03 3.046e+02 3.375 0.000816 ***
## case_count_d1.l2 -2.631e-01 4.006e-01 -0.657 0.511685
## tests_taken.l3 1.963e-04 2.843e-02 0.007 0.994493
## vaccine_doses_administered.l3 -5.240e-02 4.920e-02 -1.065 0.287579
## mobility_mean.l3 -5.690e+02 3.092e+02 -1.840 0.066560 .
## case_count_d1.l3 -4.891e-01 4.579e-01 -1.068 0.286200
## tests_taken.l4 -2.612e-02 2.813e-02 -0.929 0.353576
## vaccine_doses_administered.l4 8.887e-02 4.887e-02 1.818 0.069812 .
## mobility_mean.l4 4.106e+02 3.051e+02 1.346 0.179122
## case_count_d1.l4 -6.412e-01 4.651e-01 -1.378 0.168875
## tests_taken.l5 4.957e-03 2.798e-02 0.177 0.859493
## vaccine_doses_administered.l5 -1.002e-01 4.896e-02 -2.046 0.041491 *
## mobility_mean.l5 -2.760e+02 3.042e+02 -0.907 0.364871
## case_count_d1.l5 -4.551e-01 4.558e-01 -0.998 0.318721
## tests_taken.l6 -3.422e-03 2.819e-02 -0.121 0.903444
## vaccine_doses_administered.l6 1.475e-01 4.932e-02 2.991 0.002966 **
## mobility_mean.l6 -9.781e+01 3.041e+02 -0.322 0.747893
## case_count_d1.l6 -7.274e-01 4.551e-01 -1.598 0.110803
## tests_taken.l7 3.102e-02 2.883e-02 1.076 0.282670
## vaccine_doses_administered.l7 6.992e-01 4.962e-02 14.091 < 2e-16 ***
## mobility_mean.l7 -8.339e+02 3.026e+02 -2.755 0.006152 **
## case_count_d1.l7 -3.997e-02 3.998e-01 -0.100 0.920423
## tests_taken.l8 7.617e-04 2.908e-02 0.026 0.979117
## vaccine_doses_administered.l8 -5.634e-01 4.398e-02 -12.810 < 2e-16 ***
## mobility_mean.l8 -7.604e+01 2.735e+02 -0.278 0.781143
## case_count_d1.l8 1.090e-01 3.398e-01 0.321 0.748617
## const 6.916e+02 3.623e+03 0.191 0.848720
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 20030 on 374 degrees of freedom
## Multiple R-Squared: 0.9406, Adjusted R-squared: 0.9355
## F-statistic: 185.1 on 32 and 374 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.512e-06 5.485e-06 0.276 0.782941
## vaccine_doses_administered.l1 1.885e-05 8.118e-06 2.322 0.020767 *
## mobility_mean.l1 6.149e-01 5.095e-02 12.068 < 2e-16 ***
## case_count_d1.l1 -7.481e-05 6.435e-05 -1.162 0.245777
## tests_taken.l2 -3.554e-06 5.438e-06 -0.654 0.513759
## vaccine_doses_administered.l2 -2.611e-05 9.223e-06 -2.831 0.004885 **
## mobility_mean.l2 1.248e-01 5.714e-02 2.185 0.029531 *
## case_count_d1.l2 -1.094e-04 7.515e-05 -1.456 0.146267
## tests_taken.l3 2.837e-06 5.332e-06 0.532 0.595062
## vaccine_doses_administered.l3 1.325e-05 9.230e-06 1.435 0.151987
## mobility_mean.l3 6.513e-03 5.801e-02 0.112 0.910664
## case_count_d1.l3 -1.686e-04 8.590e-05 -1.963 0.050392 .
## tests_taken.l4 -1.322e-05 5.276e-06 -2.506 0.012618 *
## vaccine_doses_administered.l4 -2.023e-05 9.168e-06 -2.206 0.027982 *
## mobility_mean.l4 8.589e-02 5.723e-02 1.501 0.134269
## case_count_d1.l4 -1.183e-04 8.725e-05 -1.356 0.175879
## tests_taken.l5 -5.799e-06 5.249e-06 -1.105 0.269951
## vaccine_doses_administered.l5 1.870e-05 9.185e-06 2.036 0.042501 *
## mobility_mean.l5 -1.010e-01 5.707e-02 -1.770 0.077613 .
## case_count_d1.l5 -8.204e-05 8.551e-05 -0.959 0.337947
## tests_taken.l6 1.441e-06 5.288e-06 0.273 0.785333
## vaccine_doses_administered.l6 -6.599e-06 9.251e-06 -0.713 0.476127
## mobility_mean.l6 7.569e-02 5.704e-02 1.327 0.185351
## case_count_d1.l6 -1.744e-04 8.536e-05 -2.043 0.041746 *
## tests_taken.l7 -1.299e-06 5.409e-06 -0.240 0.810287
## vaccine_doses_administered.l7 -1.784e-05 9.309e-06 -1.917 0.055999 .
## mobility_mean.l7 2.708e-01 5.677e-02 4.770 2.64e-06 ***
## case_count_d1.l7 -8.357e-05 7.501e-05 -1.114 0.265916
## tests_taken.l8 4.925e-06 5.455e-06 0.903 0.367234
## vaccine_doses_administered.l8 2.115e-05 8.251e-06 2.564 0.010742 *
## mobility_mean.l8 -1.952e-01 5.131e-02 -3.804 0.000166 ***
## case_count_d1.l8 7.627e-05 6.374e-05 1.196 0.232266
## const 4.366e-02 6.797e-01 0.064 0.948815
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.757 on 374 degrees of freedom
## Multiple R-Squared: 0.7429, Adjusted R-squared: 0.7209
## F-statistic: 33.77 on 32 and 374 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count_d1:
## ==============================================
## case_count_d1 = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.163e-03 4.335e-03 0.268 0.788599
## vaccine_doses_administered.l1 2.957e-02 6.416e-03 4.608 5.58e-06 ***
## mobility_mean.l1 1.431e+02 4.027e+01 3.553 0.000430 ***
## case_count_d1.l1 -6.563e-01 5.086e-02 -12.904 < 2e-16 ***
## tests_taken.l2 6.897e-03 4.297e-03 1.605 0.109344
## vaccine_doses_administered.l2 -2.569e-02 7.289e-03 -3.525 0.000476 ***
## mobility_mean.l2 -4.031e+01 4.516e+01 -0.893 0.372659
## case_count_d1.l2 -7.422e-01 5.939e-02 -12.497 < 2e-16 ***
## tests_taken.l3 9.440e-03 4.214e-03 2.240 0.025672 *
## vaccine_doses_administered.l3 8.050e-03 7.294e-03 1.104 0.270471
## mobility_mean.l3 -2.382e+01 4.585e+01 -0.519 0.603735
## case_count_d1.l3 -6.583e-01 6.789e-02 -9.696 < 2e-16 ***
## tests_taken.l4 -1.941e-03 4.170e-03 -0.465 0.641908
## vaccine_doses_administered.l4 -8.851e-03 7.246e-03 -1.221 0.222668
## mobility_mean.l4 -9.732e+01 4.523e+01 -2.152 0.032061 *
## case_count_d1.l4 -5.614e-01 6.896e-02 -8.141 5.88e-15 ***
## tests_taken.l5 -4.108e-03 4.148e-03 -0.990 0.322663
## vaccine_doses_administered.l5 1.006e-02 7.259e-03 1.385 0.166751
## mobility_mean.l5 2.251e+01 4.510e+01 0.499 0.618078
## case_count_d1.l5 -6.381e-01 6.757e-02 -9.443 < 2e-16 ***
## tests_taken.l6 -7.054e-03 4.179e-03 -1.688 0.092242 .
## vaccine_doses_administered.l6 -8.497e-03 7.311e-03 -1.162 0.245910
## mobility_mean.l6 7.078e+01 4.508e+01 1.570 0.117266
## case_count_d1.l6 -3.599e-01 6.746e-02 -5.335 1.66e-07 ***
## tests_taken.l7 -1.052e-02 4.275e-03 -2.461 0.014298 *
## vaccine_doses_administered.l7 -2.944e-03 7.357e-03 -0.400 0.689220
## mobility_mean.l7 -2.825e+01 4.487e+01 -0.630 0.529345
## case_count_d1.l7 -3.814e-02 5.928e-02 -0.643 0.520313
## tests_taken.l8 -6.414e-04 4.311e-03 -0.149 0.881805
## vaccine_doses_administered.l8 -5.119e-03 6.520e-03 -0.785 0.432927
## mobility_mean.l8 -2.654e+01 4.055e+01 -0.654 0.513213
## case_count_d1.l8 2.403e-02 5.038e-02 0.477 0.633656
## const 1.057e+03 5.372e+02 1.967 0.049884 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2969 on 374 degrees of freedom
## Multiple R-Squared: 0.5756, Adjusted R-squared: 0.5393
## F-statistic: 15.85 on 32 and 374 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken vaccine_doses_administered mobility_mean
## tests_taken 1253878482 22092309 -3099.80
## vaccine_doses_administered 22092309 401126578 16301.17
## mobility_mean -3100 16301 14.12
## case_count_d1 626054 4299342 942.69
## case_count_d1
## tests_taken 626054.2
## vaccine_doses_administered 4299342.4
## mobility_mean 942.7
## case_count_d1 8816244.0
##
## Correlation matrix of residuals:
## tests_taken vaccine_doses_administered mobility_mean
## tests_taken 1.000000 0.03115 -0.0233
## vaccine_doses_administered 0.031151 1.00000 0.2166
## mobility_mean -0.023300 0.21663 1.0000
## case_count_d1 0.005954 0.07230 0.0845
## case_count_d1
## tests_taken 0.005954
## vaccine_doses_administered 0.072297
## mobility_mean 0.084504
## case_count_d1 1.000000
preds=predict(fit5a,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced_cases_d1)[1],1),covid_reduced_cases_d1$case_count, type = "l")
lines(seq((dim(covid_reduced_cases_d1)[1]-20),dim(covid_reduced_cases_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced_cases_d1$case_count,21), type = "l",ylim=c(-3900,4600))
lines(preds$fcst$case_count[,1],type = "l",col='blue')

short_ASE_fit5a = mean((tail(covid_reduced_cases_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2)
short_ASE_fit5a
## [1] 1690468
short_ASE_fit5a^.5
## [1] 1300.18
#7 Day RMSE of 1300.18
#Maybe try to look up rolling window version
long_ASE_fit5a = mean((tail(covid_reduced_cases_d1$case_count,21)-preds$fcst$case_count[,1])^2)
long_ASE_fit5a
## [1] 988749
long_ASE_fit5a^.5
## [1] 994.3586
#21 Day RMSE of 994.35 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest RMSE
#Test a first differenced cases only with seasonality
VARselect(covid_reduced_cases_d1,lag.max = 25,type = 'const',season = 7)
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 6 8
##
## $criteria
## 1 2 3 4 5
## AIC(n) 6.096730e+01 6.069809e+01 6.057679e+01 6.040478e+01 6.015873e+01
## HQ(n) 6.114468e+01 6.093997e+01 6.088317e+01 6.077566e+01 6.059411e+01
## SC(n) 6.141477e+01 6.130827e+01 6.134968e+01 6.134039e+01 6.125705e+01
## FPE(n) 3.004622e+26 2.295688e+26 2.033759e+26 1.712783e+26 1.339642e+26
## 6 7 8 9 10
## AIC(n) 5.984485e+01 5.979697e+01 5.956566e+01 5.958146e+01 5.960094e+01
## HQ(n) 6.034473e+01 6.036135e+01 6.019454e+01 6.027484e+01 6.035882e+01
## SC(n) 6.110588e+01 6.122071e+01 6.115211e+01 6.133063e+01 6.151283e+01
## FPE(n) 9.791971e+25 9.339747e+25 7.416529e+25 7.541602e+25 7.698485e+25
## 11 12 13 14 15
## AIC(n) 5.962148e+01 5.963612e+01 5.966610e+01 5.968912e+01 5.967635e+01
## HQ(n) 6.044386e+01 6.052301e+01 6.061749e+01 6.070501e+01 6.075673e+01
## SC(n) 6.169608e+01 6.187344e+01 6.206613e+01 6.225187e+01 6.240180e+01
## FPE(n) 7.868559e+25 7.996984e+25 8.255149e+25 8.464811e+25 8.376946e+25
## 16 17 18 19 20
## AIC(n) 5.970664e+01 5.970932e+01 5.973355e+01 5.975903e+01 5.976621e+01
## HQ(n) 6.085153e+01 6.091871e+01 6.100744e+01 6.109742e+01 6.116910e+01
## SC(n) 6.259481e+01 6.276020e+01 6.294715e+01 6.313534e+01 6.330523e+01
## FPE(n) 8.657573e+25 8.706670e+25 8.949973e+25 9.214948e+25 9.319421e+25
## 21 22 23 24 25
## AIC(n) 5.980015e+01 5.975771e+01 5.978555e+01 5.983022e+01 5.986975e+01
## HQ(n) 6.126754e+01 6.128960e+01 6.138194e+01 6.149111e+01 6.159514e+01
## SC(n) 6.350189e+01 6.362216e+01 6.381272e+01 6.402010e+01 6.422234e+01
## FPE(n) 9.684737e+25 9.328368e+25 9.643789e+25 1.014399e+26 1.062089e+26
#AIC 8, BIC 8
#Fit based on AIC
fit6a=VAR(covid_reduced_cases_d1,p=8,type="const",season = 7)
summary(fit6a)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, vaccine_doses_administered, mobility_mean, case_count_d1
## Deterministic variables: const
## Sample size: 407
## Log Likelihood: -14255.72
## Roots of the characteristic polynomial:
## 0.9841 0.9841 0.9737 0.9737 0.948 0.948 0.9274 0.9033 0.9033 0.8907 0.8907 0.849 0.849 0.795 0.795 0.7874 0.7874 0.767 0.767 0.7257 0.7257 0.7025 0.7025 0.6991 0.6767 0.6767 0.6408 0.6408 0.5814 0.5814 0.3624 0.2511
## Call:
## VAR(y = covid_reduced_cases_d1, p = 8, type = "const", season = 7L)
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 8.333e-02 5.208e-02 1.600 0.110470
## vaccine_doses_administered.l1 9.619e-02 8.482e-02 1.134 0.257499
## mobility_mean.l1 1.313e+02 5.195e+02 0.253 0.800632
## case_count_d1.l1 1.216e+00 6.421e-01 1.894 0.058977 .
## tests_taken.l2 5.396e-02 5.172e-02 1.043 0.297555
## vaccine_doses_administered.l2 -8.942e-02 1.057e-01 -0.846 0.397978
## mobility_mean.l2 4.686e+02 6.298e+02 0.744 0.457374
## case_count_d1.l2 1.477e+00 7.562e-01 1.953 0.051593 .
## tests_taken.l3 4.349e-03 5.083e-02 0.086 0.931857
## vaccine_doses_administered.l3 7.423e-02 1.045e-01 0.711 0.477782
## mobility_mean.l3 1.640e+02 6.345e+02 0.259 0.796142
## case_count_d1.l3 2.053e+00 8.540e-01 2.404 0.016697 *
## tests_taken.l4 2.094e-01 5.046e-02 4.150 4.14e-05 ***
## vaccine_doses_administered.l4 3.472e-02 1.041e-01 0.334 0.738887
## mobility_mean.l4 -1.469e+01 6.328e+02 -0.023 0.981492
## case_count_d1.l4 6.219e-01 8.717e-01 0.713 0.476021
## tests_taken.l5 1.639e-01 5.025e-02 3.262 0.001210 **
## vaccine_doses_administered.l5 1.988e-02 1.043e-01 0.191 0.848917
## mobility_mean.l5 -1.095e+02 6.305e+02 -0.174 0.862259
## case_count_d1.l5 2.469e+00 8.539e-01 2.892 0.004059 **
## tests_taken.l6 1.912e-01 5.083e-02 3.762 0.000196 ***
## vaccine_doses_administered.l6 -1.781e-01 1.048e-01 -1.699 0.090247 .
## mobility_mean.l6 -3.290e+02 6.297e+02 -0.522 0.601652
## case_count_d1.l6 1.760e+00 8.354e-01 2.107 0.035822 *
## tests_taken.l7 1.543e-01 5.197e-02 2.969 0.003187 **
## vaccine_doses_administered.l7 8.960e-02 1.063e-01 0.843 0.399956
## mobility_mean.l7 -9.509e+01 6.265e+02 -0.152 0.879442
## case_count_d1.l7 8.859e-01 7.186e-01 1.233 0.218442
## tests_taken.l8 3.202e-02 5.237e-02 0.611 0.541396
## vaccine_doses_administered.l8 -6.130e-02 8.569e-02 -0.715 0.474788
## mobility_mean.l8 -1.771e+02 5.386e+02 -0.329 0.742485
## case_count_d1.l8 3.954e-01 6.114e-01 0.647 0.518249
## const 1.195e+04 6.424e+03 1.860 0.063734 .
## sd1 -8.726e+03 1.194e+04 -0.731 0.465412
## sd2 1.527e+03 1.334e+04 0.114 0.908911
## sd3 6.752e+03 1.136e+04 0.595 0.552464
## sd4 1.006e+04 1.131e+04 0.889 0.374573
## sd5 -8.065e+03 1.318e+04 -0.612 0.540949
## sd6 1.595e+03 1.165e+04 0.137 0.891177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 35500 on 368 degrees of freedom
## Multiple R-Squared: 0.4696, Adjusted R-squared: 0.4149
## F-statistic: 8.575 on 38 and 368 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -2.152e-02 2.864e-02 -0.751 0.45291
## vaccine_doses_administered.l1 8.631e-01 4.665e-02 18.503 < 2e-16 ***
## mobility_mean.l1 1.663e+02 2.857e+02 0.582 0.56088
## case_count_d1.l1 -5.244e-01 3.531e-01 -1.485 0.13840
## tests_taken.l2 1.237e-02 2.845e-02 0.435 0.66399
## vaccine_doses_administered.l2 -1.067e-01 5.811e-02 -1.836 0.06719 .
## mobility_mean.l2 6.954e+02 3.464e+02 2.007 0.04543 *
## case_count_d1.l2 -3.295e-01 4.159e-01 -0.792 0.42869
## tests_taken.l3 -1.810e-03 2.796e-02 -0.065 0.94841
## vaccine_doses_administered.l3 -6.832e-02 5.745e-02 -1.189 0.23510
## mobility_mean.l3 -3.349e+01 3.489e+02 -0.096 0.92360
## case_count_d1.l3 -3.185e-01 4.696e-01 -0.678 0.49810
## tests_taken.l4 -2.497e-02 2.775e-02 -0.900 0.36874
## vaccine_doses_administered.l4 1.368e-01 5.723e-02 2.389 0.01738 *
## mobility_mean.l4 -3.683e+00 3.480e+02 -0.011 0.99156
## case_count_d1.l4 -2.335e-01 4.794e-01 -0.487 0.62652
## tests_taken.l5 1.212e-02 2.763e-02 0.439 0.66117
## vaccine_doses_administered.l5 -1.284e-01 5.735e-02 -2.239 0.02573 *
## mobility_mean.l5 -3.370e+02 3.467e+02 -0.972 0.33166
## case_count_d1.l5 2.113e-02 4.696e-01 0.045 0.96414
## tests_taken.l6 -1.230e-02 2.796e-02 -0.440 0.66015
## vaccine_doses_administered.l6 1.904e-01 5.766e-02 3.302 0.00105 **
## mobility_mean.l6 -3.515e+02 3.463e+02 -1.015 0.31081
## case_count_d1.l6 -5.690e-01 4.595e-01 -1.239 0.21632
## tests_taken.l7 2.763e-02 2.858e-02 0.967 0.33429
## vaccine_doses_administered.l7 5.656e-01 5.847e-02 9.672 < 2e-16 ***
## mobility_mean.l7 -2.586e+02 3.445e+02 -0.751 0.45333
## case_count_d1.l7 -2.550e-02 3.952e-01 -0.065 0.94859
## tests_taken.l8 -6.493e-03 2.880e-02 -0.225 0.82178
## vaccine_doses_administered.l8 -4.770e-01 4.713e-02 -10.121 < 2e-16 ***
## mobility_mean.l8 -1.991e+02 2.962e+02 -0.672 0.50181
## case_count_d1.l8 1.754e-01 3.363e-01 0.522 0.60227
## const 4.138e+02 3.533e+03 0.117 0.90683
## sd1 -1.872e+04 6.567e+03 -2.851 0.00460 **
## sd2 -1.070e+04 7.337e+03 -1.458 0.14570
## sd3 -8.764e+03 6.245e+03 -1.403 0.16134
## sd4 -9.777e+03 6.220e+03 -1.572 0.11685
## sd5 -2.127e+04 7.248e+03 -2.934 0.00356 **
## sd6 -2.693e+04 6.408e+03 -4.203 3.32e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 19520 on 368 degrees of freedom
## Multiple R-Squared: 0.9445, Adjusted R-squared: 0.9387
## F-statistic: 164.7 on 38 and 368 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.571e-07 5.339e-06 0.029 0.97653
## vaccine_doses_administered.l1 6.011e-06 8.695e-06 0.691 0.48976
## mobility_mean.l1 6.730e-01 5.325e-02 12.638 < 2e-16 ***
## case_count_d1.l1 -1.158e-04 6.582e-05 -1.760 0.07922 .
## tests_taken.l2 -4.497e-06 5.302e-06 -0.848 0.39692
## vaccine_doses_administered.l2 -1.146e-05 1.083e-05 -1.058 0.29067
## mobility_mean.l2 1.036e-01 6.456e-02 1.604 0.10960
## case_count_d1.l2 -1.201e-04 7.752e-05 -1.550 0.12203
## tests_taken.l3 3.565e-06 5.211e-06 0.684 0.49428
## vaccine_doses_administered.l3 7.944e-06 1.071e-05 0.742 0.45864
## mobility_mean.l3 -1.292e-02 6.504e-02 -0.199 0.84261
## case_count_d1.l3 -1.874e-04 8.754e-05 -2.141 0.03293 *
## tests_taken.l4 -1.210e-05 5.173e-06 -2.339 0.01989 *
## vaccine_doses_administered.l4 -9.375e-06 1.067e-05 -0.879 0.38011
## mobility_mean.l4 7.083e-02 6.487e-02 1.092 0.27555
## case_count_d1.l4 -1.581e-04 8.936e-05 -1.770 0.07759 .
## tests_taken.l5 -5.268e-06 5.151e-06 -1.023 0.30710
## vaccine_doses_administered.l5 1.754e-06 1.069e-05 0.164 0.86974
## mobility_mean.l5 -4.643e-02 6.463e-02 -0.718 0.47292
## case_count_d1.l5 -1.032e-04 8.753e-05 -1.179 0.23915
## tests_taken.l6 7.607e-07 5.211e-06 0.146 0.88402
## vaccine_doses_administered.l6 7.434e-06 1.075e-05 0.692 0.48960
## mobility_mean.l6 6.931e-02 6.455e-02 1.074 0.28368
## case_count_d1.l6 -1.032e-04 8.564e-05 -1.205 0.22885
## tests_taken.l7 1.017e-06 5.327e-06 0.191 0.84864
## vaccine_doses_administered.l7 -9.148e-06 1.090e-05 -0.839 0.40186
## mobility_mean.l7 1.080e-01 6.422e-02 1.682 0.09342 .
## case_count_d1.l7 -6.782e-05 7.366e-05 -0.921 0.35786
## tests_taken.l8 3.555e-06 5.369e-06 0.662 0.50828
## vaccine_doses_administered.l8 7.578e-06 8.784e-06 0.863 0.38887
## mobility_mean.l8 -7.578e-02 5.521e-02 -1.373 0.17070
## case_count_d1.l8 8.182e-05 6.268e-05 1.305 0.19258
## const 1.099e-01 6.585e-01 0.167 0.86752
## sd1 3.347e+00 1.224e+00 2.734 0.00656 **
## sd2 3.273e+00 1.368e+00 2.394 0.01719 *
## sd3 2.966e+00 1.164e+00 2.548 0.01125 *
## sd4 1.012e+00 1.159e+00 0.873 0.38313
## sd5 6.313e+00 1.351e+00 4.673 4.18e-06 ***
## sd6 1.882e+00 1.194e+00 1.576 0.11596
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.639 on 368 degrees of freedom
## Multiple R-Squared: 0.7627, Adjusted R-squared: 0.7382
## F-statistic: 31.12 on 38 and 368 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count_d1:
## ==============================================
## case_count_d1 = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 7.603e-04 4.129e-03 0.184 0.853986
## vaccine_doses_administered.l1 1.639e-02 6.724e-03 2.438 0.015253 *
## mobility_mean.l1 2.283e+02 4.118e+01 5.544 5.66e-08 ***
## case_count_d1.l1 -6.820e-01 5.090e-02 -13.399 < 2e-16 ***
## tests_taken.l2 8.266e-03 4.100e-03 2.016 0.044512 *
## vaccine_doses_administered.l2 -1.004e-02 8.376e-03 -1.199 0.231464
## mobility_mean.l2 -8.686e+01 4.993e+01 -1.740 0.082741 .
## case_count_d1.l2 -7.203e-01 5.995e-02 -12.016 < 2e-16 ***
## tests_taken.l3 1.212e-02 4.029e-03 3.007 0.002819 **
## vaccine_doses_administered.l3 1.222e-02 8.280e-03 1.475 0.141009
## mobility_mean.l3 -6.250e+01 5.029e+01 -1.243 0.214734
## case_count_d1.l3 -6.201e-01 6.769e-02 -9.161 < 2e-16 ***
## tests_taken.l4 -1.015e-03 4.000e-03 -0.254 0.799775
## vaccine_doses_administered.l4 -1.050e-02 8.249e-03 -1.273 0.203874
## mobility_mean.l4 -1.017e+02 5.016e+01 -2.028 0.043267 *
## case_count_d1.l4 -4.910e-01 6.910e-02 -7.105 6.26e-12 ***
## tests_taken.l5 -4.848e-03 3.983e-03 -1.217 0.224273
## vaccine_doses_administered.l5 4.646e-03 8.266e-03 0.562 0.574402
## mobility_mean.l5 2.415e+01 4.997e+01 0.483 0.629223
## case_count_d1.l5 -5.159e-01 6.768e-02 -7.623 2.13e-13 ***
## tests_taken.l6 -7.156e-03 4.030e-03 -1.776 0.076561 .
## vaccine_doses_administered.l6 2.992e-03 8.311e-03 0.360 0.719009
## mobility_mean.l6 -1.295e+01 4.992e+01 -0.259 0.795440
## case_count_d1.l6 -2.573e-01 6.622e-02 -3.886 0.000121 ***
## tests_taken.l7 -1.077e-02 4.119e-03 -2.614 0.009319 **
## vaccine_doses_administered.l7 -1.647e-02 8.428e-03 -1.954 0.051507 .
## mobility_mean.l7 -3.035e+01 4.966e+01 -0.611 0.541427
## case_count_d1.l7 -4.390e-02 5.696e-02 -0.771 0.441401
## tests_taken.l8 -3.422e-03 4.152e-03 -0.824 0.410326
## vaccine_doses_administered.l8 -2.441e-03 6.792e-03 -0.359 0.719539
## mobility_mean.l8 7.150e+01 4.269e+01 1.675 0.094801 .
## case_count_d1.l8 9.050e-03 4.847e-02 0.187 0.851977
## const 1.059e+03 5.092e+02 2.081 0.038163 *
## sd1 3.761e+03 9.465e+02 3.974 8.52e-05 ***
## sd2 2.966e+03 1.057e+03 2.805 0.005298 **
## sd3 1.096e+03 9.001e+02 1.218 0.224020
## sd4 1.502e+03 8.966e+02 1.675 0.094833 .
## sd5 2.191e+03 1.045e+03 2.097 0.036660 *
## sd6 -2.380e+03 9.236e+02 -2.577 0.010352 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2814 on 368 degrees of freedom
## Multiple R-Squared: 0.625, Adjusted R-squared: 0.5863
## F-statistic: 16.14 on 38 and 368 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken vaccine_doses_administered mobility_mean
## tests_taken 1.260e+09 16342922 -859.88
## vaccine_doses_administered 1.634e+07 381104275 18710.29
## mobility_mean -8.599e+02 18710 13.24
## case_count_d1 1.674e+06 2738784 503.48
## case_count_d1
## tests_taken 1673507.5
## vaccine_doses_administered 2738783.9
## mobility_mean 503.5
## case_count_d1 7917357.8
##
## Correlation matrix of residuals:
## tests_taken vaccine_doses_administered mobility_mean
## tests_taken 1.000000 0.02358 -0.006657
## vaccine_doses_administered 0.023584 1.00000 0.263391
## mobility_mean -0.006657 0.26339 1.000000
## case_count_d1 0.016755 0.04986 0.049174
## case_count_d1
## tests_taken 0.01675
## vaccine_doses_administered 0.04986
## mobility_mean 0.04917
## case_count_d1 1.00000
preds=predict(fit6a,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced_cases_d1)[1],1),covid_reduced_cases_d1$case_count, type = "l")
lines(seq((dim(covid_reduced_cases_d1)[1]-20),dim(covid_reduced_cases_d1)[1],1),preds$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced_cases_d1$case_count,21), type = "l",ylim=c(min(preds$fcst$case_count[,2]),12100))
lines(preds$fcst$case_count[,1],type = "l",col='blue')
lines(preds$fcst$case_count[,2],type = "l",col='blue',lty=2)
lines(preds$fcst$case_count[,3],type = "l",col='blue',lty=2)

short_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)[1:7]-preds$fcst$case_count[1:7,1])^2)
short_ASE_fit6a
## [1] 1289917
short_ASE_fit6a^.5
## [1] 1135.745
#7 Day RMSE of 1135.7
#Maybe try to look up rolling window version
long_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)-preds$fcst$case_count[,1])^2)
long_ASE_fit6a
## [1] 1247105
long_ASE_fit6a^.5
## [1] 1116.739
#21 Day RMSE of 1116.739 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest RMSE
Summarize VAR results
#Minimize Short 7 Day Forecast RMSE selects model fit6a (diff response with seasonality and lag of 8) - RMSE of 1135.75
(short_ASE_fit1a)^.5
## [1] 1763.689
(short_ASE_fit2a)^.5
## [1] 2066.276
(short_ASE_fit2b)^.5
## [1] 1595.717
(short_ASE_fit3a)^.5
## [1] 1278.838
(short_ASE_fit4a)^.5
## [1] 1143.21
(short_ASE_fit5a)^.5
## [1] 1300.18
(short_ASE_fit6a)^.5
## [1] 1135.745
min(short_ASE_fit1a,short_ASE_fit2a,short_ASE_fit2b,short_ASE_fit3a,short_ASE_fit4a,short_ASE_fit5a,short_ASE_fit6a)^.5
## [1] 1135.745
#Minimize Long 21 Day Forecast RMSE selects model fit3a (diff all data without seasonality lag of 8) - RMSE of 974.29
(long_ASE_fit1a)^.5
## [1] 1326.601
(long_ASE_fit2a)^.5
## [1] 1522.145
(long_ASE_fit2b)^.5
## [1] 2635.849
(long_ASE_fit3a)^.5
## [1] 974.2925
(long_ASE_fit4a)^.5
## [1] 1185.561
(long_ASE_fit5a)^.5
## [1] 994.3586
(long_ASE_fit6a)^.5
## [1] 1116.739
min(long_ASE_fit1a,long_ASE_fit2a,long_ASE_fit2b,long_ASE_fit3a,long_ASE_fit4a,long_ASE_fit5a,long_ASE_fit6a)^.5
## [1] 974.2925
#Minimize Short 7 Day Forecast AIC selects model fit6a (diff response with seasonality and lag of 8) - AIC of 7659
AIC(fit1a$varresult$case_count)
## [1] 7731.964
AIC(fit2a$varresult$case_count)
## [1] 7692.989
AIC(fit2b$varresult$case_count)
## [1] 7909.099
AIC(fit3a$varresult$case_count)
## [1] 7731.493
AIC(fit4a$varresult$case_count)
## [1] 7692.788
AIC(fit5a$varresult$case_count)
## [1] 7697.388
AIC(fit6a$varresult$case_count)
## [1] 7659.038
#Minimize Short 7 Day Forecast BIC selects model fit6a (diff response with seasonality and lag of 8) - BIC of 7819
BIC(fit1a$varresult$case_count)
## [1] 7868.347
BIC(fit2a$varresult$case_count)
## [1] 7853.439
BIC(fit2b$varresult$case_count)
## [1] 7973.513
BIC(fit3a$varresult$case_count)
## [1] 7851.831
BIC(fit4a$varresult$case_count)
## [1] 7837.194
BIC(fit5a$varresult$case_count)
## [1] 7833.688
BIC(fit6a$varresult$case_count)
## [1] 7819.39
Create MLP models
###MLP with reduced original data
#Create train and whole ts set
covid_reduced_train=covid_reduced[1:(dim(covid_reduced)[1]-21),]
covid_reduced_train$case_count <- ts(covid_reduced_train$case_count, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_train$tests_taken <- ts(covid_reduced_train$tests_taken, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_train$vaccine_doses_administered <- ts(covid_reduced_train$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_train$mobility_mean <- ts(covid_reduced_train$mobility_mean, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_ts=covid_reduced
covid_reduced_ts$case_count <- ts(covid_reduced_ts$case_count, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_ts$tests_taken <- ts(covid_reduced_ts$tests_taken, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_ts$vaccine_doses_administered <- ts(covid_reduced_ts$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
covid_reduced_ts$mobility_mean <- ts(covid_reduced_ts$mobility_mean, start = decimal_date(as.Date("2020-09-14")), frequency = 365)
#Fit model and forecast
set.seed(2)
fit_mlp1 = mlp(y = covid_reduced_train$case_count,xreg = covid_reduced_train[,c(1,3,4)],hd.auto.type = 'cv',reps = 30,comb = 'median',allow.det.season = T)
fit_mlp1
## MLP fit with 1 hidden node and 30 repetitions.
## Series modelled in differences: D1.
## Univariate lags: (7,28,49,86,345)
## 2 regressors included.
## - Regressor 1 lags: (9,16,114)
## - Regressor 2 lags: (118)
## Forecast combined using the median operator.
## MSE: 17691565.0178.
plot(fit_mlp1)

short_f_mlp1 = forecast(fit_mlp1, h = 7, xreg = covid_reduced_ts[,c(1,3,4)])
plot(short_f_mlp1,xlim=c(2021.7,2022))

plot(seq(1,7),tail(covid_reduced_ts$case_count,21)[1:7],type = "l",ylim=c(-4800,12000))
lines(seq(1,7),short_f_mlp1$mean, col = "blue",type= 'l')

short_ASE_fit_mlp1 = mean((tail(covid_reduced_ts$case_count,21)[1:7]-short_f_mlp1$mean)^2)
short_ASE_fit_mlp1^.5
## [1] 3698.237
#RMSE of 3698
long_f_mlp1 = forecast(fit_mlp1, h = 21, xreg = covid_reduced_ts[,c(1,3,4)],level=c(95))
plot(long_f_mlp1,xlim=c(2021.7,2022))

plot(long_f_mlp1$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
lines(long_f_mlp1$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid_reduced_ts$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),tail(covid_reduced_ts$case_count,21),type = "l",ylim=c(-6500,12000))
lines(seq(1,21),long_f_mlp1$mean, col = "blue",type= 'l')

long_ASE_fit_mlp1 = mean((tail(covid_reduced_ts$case_count,21)-long_f_mlp1$mean)^2)
long_ASE_fit_mlp1^.5
## [1] 4795.097
#RMSE 4795
###Use differenced repsonse set
#Create train and whole ts set
covid_reduced_cases_d1_train=covid_reduced_cases_d1[1:(dim(covid_reduced_cases_d1)[1]-21),]
covid_reduced_cases_d1_train$case_count_d1 <- ts(covid_reduced_cases_d1_train$case_count_d1, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_train$tests_taken <- ts(covid_reduced_cases_d1_train$tests_taken, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_train$vaccine_doses_administered <- ts(covid_reduced_cases_d1_train$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_train$mobility_mean <- ts(covid_reduced_cases_d1_train$mobility_mean, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_ts=covid_reduced_cases_d1
covid_reduced_cases_d1_ts$case_count_d1 <- ts(covid_reduced_cases_d1_ts$case_count_d1, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_ts$tests_taken <- ts(covid_reduced_cases_d1_ts$tests_taken, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_ts$vaccine_doses_administered <- ts(covid_reduced_cases_d1_ts$vaccine_doses_administered, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
covid_reduced_cases_d1_ts$mobility_mean <- ts(covid_reduced_cases_d1_ts$mobility_mean, start = decimal_date(as.Date("2020-09-15")), frequency = 365)
#Fit model and forecast
set.seed(2)
fit_mlp2 = mlp(y = covid_reduced_cases_d1_train$case_count_d1,xreg = covid_reduced_cases_d1_train[,c(1,2,3)],hd.auto.type = 'cv',reps = 30,comb = 'median',allow.det.season = T)
fit_mlp2
## MLP fit with 1 hidden node and 30 repetitions.
## Univariate lags: (7,28,49,86,345)
## 2 regressors included.
## - Regressor 1 lags: (9,16,114)
## - Regressor 2 lags: (118)
## Forecast combined using the median operator.
## MSE: 17691565.0178.
plot(fit_mlp2)

short_f_mlp2 = forecast(fit_mlp2, h = 7, xreg = covid_reduced_cases_d1_ts[,c(1,2,3)])
plot(short_f_mlp2,xlim=c(2021.7,2022))

plot(seq(1,7),tail(covid_reduced_cases_d1_ts$case_count_d1,21)[1:7],type = "l",ylim=c(-4800,12000))
lines(seq(1,7),short_f_mlp2$mean, col = "blue",type= 'l')

short_ASE_fit_mlp2 = mean((tail(covid_reduced_cases_d1_ts$case_count_d1,21)[1:7]-short_f_mlp2$mean)^2)
short_ASE_fit_mlp2^.5
## [1] 2760.336
#RMSE of 2760
long_f_mlp2 = forecast(fit_mlp2, h = 21, xreg = covid_reduced_cases_d1_ts[,c(1,2,3)])
plot(long_f_mlp2,xlim=c(2021.7,2022))

plot(seq(1,21),tail(covid_reduced_cases_d1_ts$case_count_d1,21),type = "l",ylim=c(-6500,12000))
lines(seq(1,21),long_f_mlp2$mean, col = "blue",type= 'l')

long_ASE_fit_mlp2 = mean((tail(covid_reduced_cases_d1_ts$case_count_d1,21)-long_f_mlp2$mean)^2)
long_ASE_fit_mlp2^.5
## [1] 5787.929
#RMSE 5788
#Selected MLP Model1
covidData = ts(covid$case_count[1:395])
covidXX = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]), park_mobility= ts(covid$parks_percent_change_from_baseline[1:395]))
covidXX_full = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered), park_mobility= ts(covid$parks_percent_change_from_baseline))
set.seed(2)
fitCOVIDXX = mlp(covidData,xreg = covidXX)
fcstCOVIDXX= forecast(fitCOVIDXX,h=21,xreg = covidXX_full)
plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
lines(seq(1,21),fcstCOVIDXX$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX$mean,col = "red")

ASE_DEEP_SHORT_XX = mean((tail(covid$case_count,21)[1:7] - fcstCOVIDXX$mean[1:7])^2)
ASE_DEEP_SHORT_XX
## [1] 907508.8
RMSE_DEEP_SHORT_XX = sqrt(ASE_DEEP_SHORT_XX)
RMSE_DEEP_SHORT_XX
## [1] 952.6326
ASE_DEEP_LONG_XX = mean((tail(covid$case_count,21) - fcstCOVIDXX$mean)^2)
ASE_DEEP_LONG_XX
## [1] 1589160
RMSE_DEEP_LONG_XX = sqrt(ASE_DEEP_LONG_XX)
RMSE_DEEP_LONG_XX
## [1] 1260.619
#Selected MLP Model2
covidData = ts(covid$case_count[1:395])
covidXX2 = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]))
covidXX_full2 = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered))
set.seed(2)
fitCOVIDXX2 = mlp(covidData,xreg = covidXX2)
fcstCOVIDXX2= forecast(fitCOVIDXX2,h=21,xreg = covidXX_full2)
plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
lines(seq(1,21),fcstCOVIDXX2$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX2$mean,col = "red")

ASE_DEEP_SHORT_XX2 = mean((tail(covid$case_count,21)[1:7] - fcstCOVIDXX2$mean[1:7])^2)
ASE_DEEP_SHORT_XX2
## [1] 2971978
RMSE_DEEP_SHORT_XX2 = sqrt(ASE_DEEP_SHORT_XX2)
RMSE_DEEP_SHORT_XX2
## [1] 1723.943
ASE_DEEP_LONG_XX2 = mean((tail(covid$case_count,21) - fcstCOVIDXX2$mean)^2)
ASE_DEEP_LONG_XX2
## [1] 5645679
RMSE_DEEP_LONG_XX2 = sqrt(ASE_DEEP_LONG_XX2)
RMSE_DEEP_LONG_XX2
## [1] 2376.064
MLP RMSE Summary
(short_ASE_fit_mlp1)^.5
## [1] 3698.237
(short_ASE_fit_mlp2)^.5
## [1] 2760.336
(long_ASE_fit_mlp1)^.5
## [1] 4795.097
(long_ASE_fit_mlp2)^.5
## [1] 5787.929
RMSE_DEEP_SHORT_XX #Selected Model For Ensemble
## [1] 952.6326
RMSE_DEEP_LONG_XX #Selected Model For Ensemble
## [1] 1260.619
RMSE_DEEP_SHORT_XX2
## [1] 1723.943
RMSE_DEEP_LONG_XX2
## [1] 2376.064
Selected MLP/VAR Models and Ensemble Model
#Selected VAR Model
#Fit based on AIC
fit6a=VAR(covid_reduced_cases_d1,p=8,type="const",season = 7)
summary(fit6a)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: tests_taken, vaccine_doses_administered, mobility_mean, case_count_d1
## Deterministic variables: const
## Sample size: 407
## Log Likelihood: -14255.72
## Roots of the characteristic polynomial:
## 0.9841 0.9841 0.9737 0.9737 0.948 0.948 0.9274 0.9033 0.9033 0.8907 0.8907 0.849 0.849 0.795 0.795 0.7874 0.7874 0.767 0.767 0.7257 0.7257 0.7025 0.7025 0.6991 0.6767 0.6767 0.6408 0.6408 0.5814 0.5814 0.3624 0.2511
## Call:
## VAR(y = covid_reduced_cases_d1, p = 8, type = "const", season = 7L)
##
##
## Estimation results for equation tests_taken:
## ============================================
## tests_taken = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 8.333e-02 5.208e-02 1.600 0.110470
## vaccine_doses_administered.l1 9.619e-02 8.482e-02 1.134 0.257499
## mobility_mean.l1 1.313e+02 5.195e+02 0.253 0.800632
## case_count_d1.l1 1.216e+00 6.421e-01 1.894 0.058977 .
## tests_taken.l2 5.396e-02 5.172e-02 1.043 0.297555
## vaccine_doses_administered.l2 -8.942e-02 1.057e-01 -0.846 0.397978
## mobility_mean.l2 4.686e+02 6.298e+02 0.744 0.457374
## case_count_d1.l2 1.477e+00 7.562e-01 1.953 0.051593 .
## tests_taken.l3 4.349e-03 5.083e-02 0.086 0.931857
## vaccine_doses_administered.l3 7.423e-02 1.045e-01 0.711 0.477782
## mobility_mean.l3 1.640e+02 6.345e+02 0.259 0.796142
## case_count_d1.l3 2.053e+00 8.540e-01 2.404 0.016697 *
## tests_taken.l4 2.094e-01 5.046e-02 4.150 4.14e-05 ***
## vaccine_doses_administered.l4 3.472e-02 1.041e-01 0.334 0.738887
## mobility_mean.l4 -1.469e+01 6.328e+02 -0.023 0.981492
## case_count_d1.l4 6.219e-01 8.717e-01 0.713 0.476021
## tests_taken.l5 1.639e-01 5.025e-02 3.262 0.001210 **
## vaccine_doses_administered.l5 1.988e-02 1.043e-01 0.191 0.848917
## mobility_mean.l5 -1.095e+02 6.305e+02 -0.174 0.862259
## case_count_d1.l5 2.469e+00 8.539e-01 2.892 0.004059 **
## tests_taken.l6 1.912e-01 5.083e-02 3.762 0.000196 ***
## vaccine_doses_administered.l6 -1.781e-01 1.048e-01 -1.699 0.090247 .
## mobility_mean.l6 -3.290e+02 6.297e+02 -0.522 0.601652
## case_count_d1.l6 1.760e+00 8.354e-01 2.107 0.035822 *
## tests_taken.l7 1.543e-01 5.197e-02 2.969 0.003187 **
## vaccine_doses_administered.l7 8.960e-02 1.063e-01 0.843 0.399956
## mobility_mean.l7 -9.509e+01 6.265e+02 -0.152 0.879442
## case_count_d1.l7 8.859e-01 7.186e-01 1.233 0.218442
## tests_taken.l8 3.202e-02 5.237e-02 0.611 0.541396
## vaccine_doses_administered.l8 -6.130e-02 8.569e-02 -0.715 0.474788
## mobility_mean.l8 -1.771e+02 5.386e+02 -0.329 0.742485
## case_count_d1.l8 3.954e-01 6.114e-01 0.647 0.518249
## const 1.195e+04 6.424e+03 1.860 0.063734 .
## sd1 -8.726e+03 1.194e+04 -0.731 0.465412
## sd2 1.527e+03 1.334e+04 0.114 0.908911
## sd3 6.752e+03 1.136e+04 0.595 0.552464
## sd4 1.006e+04 1.131e+04 0.889 0.374573
## sd5 -8.065e+03 1.318e+04 -0.612 0.540949
## sd6 1.595e+03 1.165e+04 0.137 0.891177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 35500 on 368 degrees of freedom
## Multiple R-Squared: 0.4696, Adjusted R-squared: 0.4149
## F-statistic: 8.575 on 38 and 368 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation vaccine_doses_administered:
## ===========================================================
## vaccine_doses_administered = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 -2.152e-02 2.864e-02 -0.751 0.45291
## vaccine_doses_administered.l1 8.631e-01 4.665e-02 18.503 < 2e-16 ***
## mobility_mean.l1 1.663e+02 2.857e+02 0.582 0.56088
## case_count_d1.l1 -5.244e-01 3.531e-01 -1.485 0.13840
## tests_taken.l2 1.237e-02 2.845e-02 0.435 0.66399
## vaccine_doses_administered.l2 -1.067e-01 5.811e-02 -1.836 0.06719 .
## mobility_mean.l2 6.954e+02 3.464e+02 2.007 0.04543 *
## case_count_d1.l2 -3.295e-01 4.159e-01 -0.792 0.42869
## tests_taken.l3 -1.810e-03 2.796e-02 -0.065 0.94841
## vaccine_doses_administered.l3 -6.832e-02 5.745e-02 -1.189 0.23510
## mobility_mean.l3 -3.349e+01 3.489e+02 -0.096 0.92360
## case_count_d1.l3 -3.185e-01 4.696e-01 -0.678 0.49810
## tests_taken.l4 -2.497e-02 2.775e-02 -0.900 0.36874
## vaccine_doses_administered.l4 1.368e-01 5.723e-02 2.389 0.01738 *
## mobility_mean.l4 -3.683e+00 3.480e+02 -0.011 0.99156
## case_count_d1.l4 -2.335e-01 4.794e-01 -0.487 0.62652
## tests_taken.l5 1.212e-02 2.763e-02 0.439 0.66117
## vaccine_doses_administered.l5 -1.284e-01 5.735e-02 -2.239 0.02573 *
## mobility_mean.l5 -3.370e+02 3.467e+02 -0.972 0.33166
## case_count_d1.l5 2.113e-02 4.696e-01 0.045 0.96414
## tests_taken.l6 -1.230e-02 2.796e-02 -0.440 0.66015
## vaccine_doses_administered.l6 1.904e-01 5.766e-02 3.302 0.00105 **
## mobility_mean.l6 -3.515e+02 3.463e+02 -1.015 0.31081
## case_count_d1.l6 -5.690e-01 4.595e-01 -1.239 0.21632
## tests_taken.l7 2.763e-02 2.858e-02 0.967 0.33429
## vaccine_doses_administered.l7 5.656e-01 5.847e-02 9.672 < 2e-16 ***
## mobility_mean.l7 -2.586e+02 3.445e+02 -0.751 0.45333
## case_count_d1.l7 -2.550e-02 3.952e-01 -0.065 0.94859
## tests_taken.l8 -6.493e-03 2.880e-02 -0.225 0.82178
## vaccine_doses_administered.l8 -4.770e-01 4.713e-02 -10.121 < 2e-16 ***
## mobility_mean.l8 -1.991e+02 2.962e+02 -0.672 0.50181
## case_count_d1.l8 1.754e-01 3.363e-01 0.522 0.60227
## const 4.138e+02 3.533e+03 0.117 0.90683
## sd1 -1.872e+04 6.567e+03 -2.851 0.00460 **
## sd2 -1.070e+04 7.337e+03 -1.458 0.14570
## sd3 -8.764e+03 6.245e+03 -1.403 0.16134
## sd4 -9.777e+03 6.220e+03 -1.572 0.11685
## sd5 -2.127e+04 7.248e+03 -2.934 0.00356 **
## sd6 -2.693e+04 6.408e+03 -4.203 3.32e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 19520 on 368 degrees of freedom
## Multiple R-Squared: 0.9445, Adjusted R-squared: 0.9387
## F-statistic: 164.7 on 38 and 368 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation mobility_mean:
## ==============================================
## mobility_mean = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 1.571e-07 5.339e-06 0.029 0.97653
## vaccine_doses_administered.l1 6.011e-06 8.695e-06 0.691 0.48976
## mobility_mean.l1 6.730e-01 5.325e-02 12.638 < 2e-16 ***
## case_count_d1.l1 -1.158e-04 6.582e-05 -1.760 0.07922 .
## tests_taken.l2 -4.497e-06 5.302e-06 -0.848 0.39692
## vaccine_doses_administered.l2 -1.146e-05 1.083e-05 -1.058 0.29067
## mobility_mean.l2 1.036e-01 6.456e-02 1.604 0.10960
## case_count_d1.l2 -1.201e-04 7.752e-05 -1.550 0.12203
## tests_taken.l3 3.565e-06 5.211e-06 0.684 0.49428
## vaccine_doses_administered.l3 7.944e-06 1.071e-05 0.742 0.45864
## mobility_mean.l3 -1.292e-02 6.504e-02 -0.199 0.84261
## case_count_d1.l3 -1.874e-04 8.754e-05 -2.141 0.03293 *
## tests_taken.l4 -1.210e-05 5.173e-06 -2.339 0.01989 *
## vaccine_doses_administered.l4 -9.375e-06 1.067e-05 -0.879 0.38011
## mobility_mean.l4 7.083e-02 6.487e-02 1.092 0.27555
## case_count_d1.l4 -1.581e-04 8.936e-05 -1.770 0.07759 .
## tests_taken.l5 -5.268e-06 5.151e-06 -1.023 0.30710
## vaccine_doses_administered.l5 1.754e-06 1.069e-05 0.164 0.86974
## mobility_mean.l5 -4.643e-02 6.463e-02 -0.718 0.47292
## case_count_d1.l5 -1.032e-04 8.753e-05 -1.179 0.23915
## tests_taken.l6 7.607e-07 5.211e-06 0.146 0.88402
## vaccine_doses_administered.l6 7.434e-06 1.075e-05 0.692 0.48960
## mobility_mean.l6 6.931e-02 6.455e-02 1.074 0.28368
## case_count_d1.l6 -1.032e-04 8.564e-05 -1.205 0.22885
## tests_taken.l7 1.017e-06 5.327e-06 0.191 0.84864
## vaccine_doses_administered.l7 -9.148e-06 1.090e-05 -0.839 0.40186
## mobility_mean.l7 1.080e-01 6.422e-02 1.682 0.09342 .
## case_count_d1.l7 -6.782e-05 7.366e-05 -0.921 0.35786
## tests_taken.l8 3.555e-06 5.369e-06 0.662 0.50828
## vaccine_doses_administered.l8 7.578e-06 8.784e-06 0.863 0.38887
## mobility_mean.l8 -7.578e-02 5.521e-02 -1.373 0.17070
## case_count_d1.l8 8.182e-05 6.268e-05 1.305 0.19258
## const 1.099e-01 6.585e-01 0.167 0.86752
## sd1 3.347e+00 1.224e+00 2.734 0.00656 **
## sd2 3.273e+00 1.368e+00 2.394 0.01719 *
## sd3 2.966e+00 1.164e+00 2.548 0.01125 *
## sd4 1.012e+00 1.159e+00 0.873 0.38313
## sd5 6.313e+00 1.351e+00 4.673 4.18e-06 ***
## sd6 1.882e+00 1.194e+00 1.576 0.11596
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 3.639 on 368 degrees of freedom
## Multiple R-Squared: 0.7627, Adjusted R-squared: 0.7382
## F-statistic: 31.12 on 38 and 368 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation case_count_d1:
## ==============================================
## case_count_d1 = tests_taken.l1 + vaccine_doses_administered.l1 + mobility_mean.l1 + case_count_d1.l1 + tests_taken.l2 + vaccine_doses_administered.l2 + mobility_mean.l2 + case_count_d1.l2 + tests_taken.l3 + vaccine_doses_administered.l3 + mobility_mean.l3 + case_count_d1.l3 + tests_taken.l4 + vaccine_doses_administered.l4 + mobility_mean.l4 + case_count_d1.l4 + tests_taken.l5 + vaccine_doses_administered.l5 + mobility_mean.l5 + case_count_d1.l5 + tests_taken.l6 + vaccine_doses_administered.l6 + mobility_mean.l6 + case_count_d1.l6 + tests_taken.l7 + vaccine_doses_administered.l7 + mobility_mean.l7 + case_count_d1.l7 + tests_taken.l8 + vaccine_doses_administered.l8 + mobility_mean.l8 + case_count_d1.l8 + const + sd1 + sd2 + sd3 + sd4 + sd5 + sd6
##
## Estimate Std. Error t value Pr(>|t|)
## tests_taken.l1 7.603e-04 4.129e-03 0.184 0.853986
## vaccine_doses_administered.l1 1.639e-02 6.724e-03 2.438 0.015253 *
## mobility_mean.l1 2.283e+02 4.118e+01 5.544 5.66e-08 ***
## case_count_d1.l1 -6.820e-01 5.090e-02 -13.399 < 2e-16 ***
## tests_taken.l2 8.266e-03 4.100e-03 2.016 0.044512 *
## vaccine_doses_administered.l2 -1.004e-02 8.376e-03 -1.199 0.231464
## mobility_mean.l2 -8.686e+01 4.993e+01 -1.740 0.082741 .
## case_count_d1.l2 -7.203e-01 5.995e-02 -12.016 < 2e-16 ***
## tests_taken.l3 1.212e-02 4.029e-03 3.007 0.002819 **
## vaccine_doses_administered.l3 1.222e-02 8.280e-03 1.475 0.141009
## mobility_mean.l3 -6.250e+01 5.029e+01 -1.243 0.214734
## case_count_d1.l3 -6.201e-01 6.769e-02 -9.161 < 2e-16 ***
## tests_taken.l4 -1.015e-03 4.000e-03 -0.254 0.799775
## vaccine_doses_administered.l4 -1.050e-02 8.249e-03 -1.273 0.203874
## mobility_mean.l4 -1.017e+02 5.016e+01 -2.028 0.043267 *
## case_count_d1.l4 -4.910e-01 6.910e-02 -7.105 6.26e-12 ***
## tests_taken.l5 -4.848e-03 3.983e-03 -1.217 0.224273
## vaccine_doses_administered.l5 4.646e-03 8.266e-03 0.562 0.574402
## mobility_mean.l5 2.415e+01 4.997e+01 0.483 0.629223
## case_count_d1.l5 -5.159e-01 6.768e-02 -7.623 2.13e-13 ***
## tests_taken.l6 -7.156e-03 4.030e-03 -1.776 0.076561 .
## vaccine_doses_administered.l6 2.992e-03 8.311e-03 0.360 0.719009
## mobility_mean.l6 -1.295e+01 4.992e+01 -0.259 0.795440
## case_count_d1.l6 -2.573e-01 6.622e-02 -3.886 0.000121 ***
## tests_taken.l7 -1.077e-02 4.119e-03 -2.614 0.009319 **
## vaccine_doses_administered.l7 -1.647e-02 8.428e-03 -1.954 0.051507 .
## mobility_mean.l7 -3.035e+01 4.966e+01 -0.611 0.541427
## case_count_d1.l7 -4.390e-02 5.696e-02 -0.771 0.441401
## tests_taken.l8 -3.422e-03 4.152e-03 -0.824 0.410326
## vaccine_doses_administered.l8 -2.441e-03 6.792e-03 -0.359 0.719539
## mobility_mean.l8 7.150e+01 4.269e+01 1.675 0.094801 .
## case_count_d1.l8 9.050e-03 4.847e-02 0.187 0.851977
## const 1.059e+03 5.092e+02 2.081 0.038163 *
## sd1 3.761e+03 9.465e+02 3.974 8.52e-05 ***
## sd2 2.966e+03 1.057e+03 2.805 0.005298 **
## sd3 1.096e+03 9.001e+02 1.218 0.224020
## sd4 1.502e+03 8.966e+02 1.675 0.094833 .
## sd5 2.191e+03 1.045e+03 2.097 0.036660 *
## sd6 -2.380e+03 9.236e+02 -2.577 0.010352 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2814 on 368 degrees of freedom
## Multiple R-Squared: 0.625, Adjusted R-squared: 0.5863
## F-statistic: 16.14 on 38 and 368 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## tests_taken vaccine_doses_administered mobility_mean
## tests_taken 1.260e+09 16342922 -859.88
## vaccine_doses_administered 1.634e+07 381104275 18710.29
## mobility_mean -8.599e+02 18710 13.24
## case_count_d1 1.674e+06 2738784 503.48
## case_count_d1
## tests_taken 1673507.5
## vaccine_doses_administered 2738783.9
## mobility_mean 503.5
## case_count_d1 7917357.8
##
## Correlation matrix of residuals:
## tests_taken vaccine_doses_administered mobility_mean
## tests_taken 1.000000 0.02358 -0.006657
## vaccine_doses_administered 0.023584 1.00000 0.263391
## mobility_mean -0.006657 0.26339 1.000000
## case_count_d1 0.016755 0.04986 0.049174
## case_count_d1
## tests_taken 0.01675
## vaccine_doses_administered 0.04986
## mobility_mean 0.04917
## case_count_d1 1.00000
preds_6a=predict(fit6a,n.ahead=21)
par(mfrow=c(1,1))
#Fan charts
fanchart(preds_6a, colors = brewer.pal(n = 8, name = "Blues"))

#Entire Plot
plot(seq(1,dim(covid_reduced_cases_d1)[1],1),covid_reduced_cases_d1$case_count, type = "l")
lines(seq((dim(covid_reduced_cases_d1)[1]-20),dim(covid_reduced_cases_d1)[1],1),preds_6a$fcst$case_count[,1],type = "l",col='blue')

#Visualize only forecasted points
plot(tail(covid_reduced_cases_d1$case_count,21), type = "l",ylim=c(min(preds_6a$fcst$case_count[,2]),12100))
lines(preds_6a$fcst$case_count[,1],type = "l",col='blue')
lines(preds_6a$fcst$case_count[,2],type = "l",col='blue',lty=2)
lines(preds_6a$fcst$case_count[,3],type = "l",col='blue',lty=2)

short_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)[1:7]-preds_6a$fcst$case_count[1:7,1])^2)
short_ASE_fit6a
## [1] 1289917
short_ASE_fit6a^.5
## [1] 1135.745
#7 Day RMSE of 1135.7
#Maybe try to look up rolling window version
long_ASE_fit6a = mean((tail(covid_reduced_cases_d1$case_count,21)-preds_6a$fcst$case_count[,1])^2)
long_ASE_fit6a
## [1] 1247105
long_ASE_fit6a^.5
## [1] 1116.739
#21 Day RMSE of 1116.739 which is much lower than the 3806 from our ARIMA(6,1,14) model and lowest RMSE
#Selected MLP Model1
covidData = ts(covid$case_count[1:395])
covidXX = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]), park_mobility= ts(covid$parks_percent_change_from_baseline[1:395]))
covidXX_full = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered), park_mobility= ts(covid$parks_percent_change_from_baseline))
set.seed(2)
fitCOVIDXX = mlp(covidData,xreg = covidXX)
fcstCOVIDXX= forecast(fitCOVIDXX,h=21,xreg = covidXX_full)
plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
lines(seq(1,21),fcstCOVIDXX$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX$mean,col = "red")

ASE_DEEP_LONG_XX = mean((tail(covid$case_count,21) - fcstCOVIDXX$mean)^2)
ASE_DEEP_LONG_XX
## [1] 1589160
RMSE_DEEP_LONG_XX = sqrt(ASE_DEEP_LONG_XX)
RMSE_DEEP_LONG_XX
## [1] 1260.619
#Selected MLP Model2
covidData = ts(covid$case_count[1:395])
covidXX2 = data.frame(testsTS = ts(covid$tests_taken[1:395]), vaccinesTS = ts(covid$vaccine_doses_administered[1:395]))
covidXX_full2 = data.frame(testsTS = ts(covid$tests_taken), vaccinesTS = ts(covid$vaccine_doses_administered))
set.seed(2)
fitCOVIDXX2 = mlp(covidData,xreg = covidXX2)
fcstCOVIDXX2= forecast(fitCOVIDXX2,h=21,xreg = covidXX_full2)
plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
for (i in 1:20){
lines(seq(1,21),fcstCOVIDXX2$all.mean[,i],col = 'grey',type = 'l')
}
lines(tail(covid$case_count,21),type = "l",col='blue',lwd=5)

plot(seq(1,21),fcstCOVIDXX2$mean,type='l',ylim=c(-20000,20000),lwd=5)
lines(seq(1,21),fcstCOVIDXX2$mean,col = "red")

ASE_DEEP_LONG_XX2 = mean((tail(covid$case_count,21) - fcstCOVIDXX2$mean)^2)
ASE_DEEP_LONG_XX2
## [1] 5645679
RMSE_DEEP_LONG_XX2 = sqrt(ASE_DEEP_LONG_XX)
RMSE_DEEP_LONG_XX2
## [1] 1260.619
#Ensemble forecast
adj_preds2=preds_6a$fcst$case_count_d1[,1]+tail(covid$case_count,22)[1:21]
plot(adj_preds2,type='l',ylim=c(-10000,10000))
lines(tail(covid$case_count,21),col='blue')

adj_ASE_6a = mean((tail(covid$case_count,21)-adj_preds2)^2)
adj_ASE_6a^.5
## [1] 1116.739
ensemble_preds=(adj_preds2+fcstCOVIDXX$mean)/2
plot(tail(covid$case_count,21),type='l',ylim=c(-10000,10000))
lines(seq(1,21),tail(ensemble_preds,21),col='blue')

ensemble_ASE = mean((tail(covid$case_count,21)[1:7]-ensemble_preds[1:7])^2)
ensemble_ASE^.5
## [1] 903.0232
ensemble_ASE = mean((tail(covid$case_count,21)-ensemble_preds)^2)
ensemble_ASE^.5
## [1] 1031.55
#Final comparison plot
plot(tail(covid$case_count,21),type='l',ylim=c(0,7000),lwd=4)
lines(adj_preds2,type = "l",col='grey')
lines(seq(1,21),fcstCOVIDXX$mean,col = "grey")
lines(seq(1,21),tail(ensemble_preds,21),col='blue',lwd=2,lty=2)

#Final comparison plot
plot(tail(covid$case_count,100),type='l',ylim=c(0,30000),lwd=2)
lines(seq(80,100),adj_preds2,type = "l",col='dark grey')
lines(seq(80,100),fcstCOVIDXX$mean,col = "dark grey")
lines(seq(80,100),tail(ensemble_preds,21),col='blue',lwd=2,lty=2)
